\u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0902 \u0914\u0930 \u092a\u0940\u092f\u093e\u0928\u094b \u0915\u0947 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924<\/title> <\/head> <body> <\/p>\n<div style=\" padding:20px;\"><center><\/p>\n<h1>\u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0902 \u0914\u0930 \u092a\u0940\u092f\u093e\u0928\u094b \u0915\u0947 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924<\/h1>\n\u0938\u093e\u0930\u093e\u0902\u0936<\/b> \n\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0914\u0930 \u092a\u0940\u092f\u093e\u0928\u094b \u0915\u0947 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924\u094b\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0909\u0928\u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u092a\u0930 \u091a\u0930\u094d\u091a\u093e \u0915\u0940 \u0917\u0908 \u0939\u0948: \u0915\u0941\u091b \u0917\u0923\u093f\u0924\u0940\u092f \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u091c\u094b \u0909\u0928\u0915\u0947 \u092e\u094c\u0932\u093f\u0915 \u0917\u0941\u0923\u094b\u0902 \u0915\u094b \u0938\u094d\u0925\u093f\u0930 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u092f\u0939 \u092d\u0940 \u092c\u0924\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0909\u0924\u094d\u0924\u0930\u093e\u0927\u093f\u0915\u093e\u0930\u093f\u092f\u094b\u0902 \u0915\u094b \u092a\u094d\u0930\u0924\u093f\u0937\u094d\u0920\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092a\u094d\u0930\u0924\u0940\u0915 \u0915\u0948\u0938\u0947 \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0935\u0947 \u092a\u094d\u0930\u0924\u0940\u0915\u093e\u0924\u094d\u092e\u0915 \u0930\u0942\u092a \u0938\u0947 \u0915\u0948\u0938\u0947 \u092a\u094d\u0930\u0924\u093f\u0937\u094d\u0920\u093f\u0924 \u0915\u093f\u090f \u091c\u093e\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u092a\u094d\u0930\u0947\u0930\u0923\u093e \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0948\u0938\u0947 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0917\u0923\u093f\u0924\u0940\u092f \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u092a\u094d\u0930\u0947\u0930\u0923\u093e\u0924\u094d\u092e\u0915 \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f\u0964<\/em><\/p>\n\u0905\u0927\u093f\u0917\u092e \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f<\/b><\/p>\n<\/center><\/p>\n<ol>\n<li>\u092a\u0940\u092f\u093e\u0928\u094b \u0915\u0947 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924\u094b\u0902 \u0915\u094b<\/strong> \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u092b\u093e\u0930\u094d\u092e\u0942\u0932\u093e \u0915\u0947 \u0932\u093f\u090f \u0938\u092e\u091d\u0947\u0902\u0964<\/li>\n<li>\u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u092a\u094d\u0930\u0924\u0940\u0915\u093e\u0924\u094d\u092e\u0915 \u092a\u094d\u0930\u0924\u093f\u0937\u094d\u0920\u093e\u0928<\/strong> \u0915\u0947 \u092b\u093e\u0930\u094d\u092e\u0942\u0932\u093e \u0915\u094b \u0938\u092e\u091d\u0947\u0902\u0964 <\/li>\n<\/ol>\n<center><\/p>\n\u0938\u0942\u091a\u0940<\/strong><\/p>\n\n<a href=\"#1\">\u092a\u0940\u092f\u093e\u0928\u094b \u0915\u0947 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0932\u093f\u090f<\/strong><\/a> \n<a href=\"#2\">\u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u092e\u0947\u0902 \u092a\u094d\u0930\u0947\u0930\u0923\u093e \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924<\/strong><\/a> \n<a href=\"#3\">\u092a\u094d\u0930\u092e\u093e\u0923 \u092a\u0930 \u091f\u093f\u092a\u094d\u092a\u0923\u0940<\/a><\/p>\n<\/center><\/p>\n<center> \n<iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/w-BznjX88No\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe> \n<\/center><\/div>\n<a name=\"1\"><\/a><\/p>\n<h2>\u092a\u0940\u092f\u093e\u0928\u094b \u0915\u0947 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0932\u093f\u090f<\/h2>\n\u091c\u094b \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0902<\/em>, \u091c\u093f\u0938\u0947 \u0938\u0915\u093e\u0930\u093e\u0924\u094d\u092e\u0915 \u092a\u0942\u0930\u094d\u0923 \u0938\u0902\u0916\u094d\u092f\u093e<\/em> \u092d\u0940 \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0935\u0947 \u0939\u0948\u0902 \u091c\u093f\u0928\u094d\u0939\u0947\u0902 \u0939\u092e \u0917\u093f\u0928\u0924\u0940 \u0914\u0930 \u092e\u093e\u092a\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u092f\u0939 \u0917\u093f\u0928\u0924\u0940 \u0915\u0940 \u0915\u094d\u0930\u093f\u092f\u093e \u092e\u0947\u0902 \u0938\u092c\u0938\u0947 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0930\u0942\u092a \u0938\u0947 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0939\u094b\u0924\u093e \u0939\u0948, \u091c\u094b \u0917\u0923\u093f\u0924 \u0915\u0940 \u0938\u092c\u0938\u0947 \u0938\u0930\u0932 \u0915\u094d\u0930\u093f\u092f\u093e \u0939\u0948\u0964 \u0907\u0928 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u092a\u0940\u092f\u093e\u0928\u094b \u0915\u0947 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924<\/em><\/strong> \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u090f\u0915 \u0910\u0938\u093e \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u091c\u094b \u092f\u0947 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 \u0915\u093f \u092f\u0947 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0902 \u0915\u0948\u0938\u0947 \u0915\u093e\u092e \u0915\u0930\u0924\u0940 \u0939\u0948\u0902\u0964<\/p>\n<ol style=\"text-align: justify;\">\n<li>\u00ab1<\/span>\u00bb \u090f\u0915 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948<\/li>\n<li>\u0905\u0917\u0930 n<\/span> \u090f\u0915 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0939\u0948, \u0924\u094b \u0909\u0938\u0915\u093e \u0909\u0924\u094d\u0924\u0930\u093e\u0927\u093f\u0915\u093e\u0930\u0940 S(n)<\/span> \u092d\u0940 \u0939\u0948\u0964<\/li>\n<li>\u00ab1<\/span>\u00bb \u0915\u093f\u0938\u0940 \u092d\u0940 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u093e \u0909\u0924\u094d\u0924\u0930\u093e\u0927\u093f\u0915\u093e\u0930\u0940 \u0928\u0939\u0940\u0902 \u0939\u0948\u0964<\/li>\n<li>\u0905\u0917\u0930 S(n) = S(m)<\/span>, \u0924\u094b n=m<\/span>\u0964<\/li>\n<li>\u0905\u0917\u0930 1<\/span> \u0915\u093f\u0938\u0940 \u0938\u092e\u0942\u0939 A<\/span> \u0915\u093e \u0939\u093f\u0938\u094d\u0938\u093e \u0939\u0948; \u0914\u0930 \u0905\u0917\u0930 \u0915\u093f\u0938\u0940 \u092d\u0940 k<\/span> \u0915\u0947 \u0932\u093f\u090f A<\/span> \u092e\u0947\u0902, S(k)<\/span> \u092d\u0940 A<\/span> \u092e\u0947\u0902 \u0939\u0948, \u0924\u094b A<\/span> \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u093e \u0938\u092e\u0942\u0939 \u0939\u0948 \u0914\u0930 \u0907\u0938\u0947 \\mathbb{N}<\/span> \u0926\u094d\u0935\u093e\u0930\u093e \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/li>\n<\/ol>\n\u092a\u0940\u092f\u093e\u0928\u094b \u0915\u0947 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924\u094b\u0902 \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0924\u0947 \u0938\u092e\u092f \u0939\u092e \u092f\u0939 \u0938\u092e\u091d\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u092a\u094d\u0930\u0924\u0940\u0915 \u00ab1<\/span>\u00bb \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902 \u0915\u0947\u0935\u0932 \u090f\u0915 \u0935\u093f\u0936\u093f\u0937\u094d\u091f \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b \u0938\u0942\u091a\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b \u0907\u0928 \u0917\u0941\u0923\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 \u092a\u0942\u0930\u093e \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u091c\u0948\u0938\u0947 1<\/span> \u00ab\u092a\u0939\u0932\u0947 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915\u00bb \u0915\u094b \u092a\u094d\u0930\u0924\u093f\u0937\u094d\u0920\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948, \u0939\u092e \u0909\u0938\u0915\u0947 \u0909\u0924\u094d\u0924\u0930\u093e\u0927\u093f\u0915\u093e\u0930\u093f\u092f\u094b\u0902 \u0915\u094b \u092a\u094d\u0930\u0924\u093f\u0937\u094d\u0920\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092a\u094d\u0930\u0924\u0940\u0915\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 (\u091c\u094b \u0939\u092e\u093e\u0930\u0947 \u0932\u093f\u090f \u092a\u0930\u093f\u091a\u093f\u0924 \u0939\u0948\u0902)\u0964 <\/p>\n<ul style=\"text-align: justify;\">\n<li>2=S(1)<\/span><\/li>\n<li>3=S(2)<\/span><\/li>\n<li>4=S(3) \\\\ \\vdots<\/span><\/li>\n<\/ul>\n\u0914\u0930 \u0907\u0938\u0940 \u0924\u0930\u0939\u0964 \u0907\u0938 \u0924\u0930\u0939, \u092a\u094d\u0930\u0924\u0940\u0915 1<\/span>, 2<\/span>, 3<\/span>, \u0906\u0926\u093f … \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902 1<\/span> \u0915\u0947 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0909\u0924\u094d\u0924\u0930\u093e\u0927\u093f\u0915\u093e\u0930\u0940 \u0939\u0948\u0902\u0964 \u0907\u0928 \u0938\u092d\u0940 \u0935\u0938\u094d\u0924\u094d\u0930\u094b\u0902 \u0915\u093e \u0938\u0902\u0917\u094d\u0930\u0939 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948 \u0914\u0930 \u0939\u092e \u0907\u0938\u0947 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0924\u0930\u0940\u0915\u0947 \u0938\u0947 \u092a\u094d\u0930\u0924\u093f\u0937\u094d\u0920\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902:<\/p>\n\\mathbb{N}=\\{1,2,3,4,\\cdots \\}<\/span>\n\u092f\u0939 \u092d\u0940 \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0902 \u090f\u0915 \u0905\u0928\u0941\u0915\u094d\u0930\u092e \u092e\u0947\u0902 \u0930\u0916\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0902, \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u093e \u0905\u0928\u0941\u0915\u094d\u0930\u092e:<\/p>\n1,2,3,4,5,6,7,8,9,10,11,12, \\cdots <\/span>\n<a name=\"2\"><\/a><\/p>\n<h2>\u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u092e\u0947\u0902 \u092a\u094d\u0930\u0947\u0930\u0923\u093e \u0915\u093e \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924<\/h2>\n\u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u093e \u090f\u0915 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092a\u0939\u0932\u0941 \u0939\u0948 \u0915\u093f \u0939\u0930 \u090f\u0915 \u0915\u0947 \u092c\u093e\u0926 \u0939\u092e\u0947\u0936\u093e \u090f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u094b\u0924\u0940 \u0939\u0948, \u0907\u0938\u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u0948 \u0915\u093f \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0940 \u0905\u0928\u0902\u0924 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948\u0964 \u0939\u092e \u0907\u0938\u0947 \u092a\u093e\u0901\u091a\u0935\u0947 \u0905\u0915\u094d\u0937\u0930 \u0938\u0947 \u0905\u0928\u0941\u092e\u093e\u0928 \u0932\u0917\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u092f\u093e \u092a\u094d\u0930\u0947\u0930\u0923\u093e \u0915\u093e \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924,<\/strong> \u091c\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0924\u0930\u0940\u0915\u0947 \u0938\u0947 \u0935\u094d\u092f\u0915\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n\u092f\u0926\u093f \u0915\u093f\u0938\u0940 \u0917\u0941\u0923 \u0915\u094b 1<\/span> \u0915\u0947 \u0932\u093f\u090f \u0938\u0924\u094d\u092f \u092e\u093e\u0928\u093e \u091c\u093e\u090f; \u0914\u0930 \u092f\u0926\u093f \u0938\u094d\u0935\u0940\u0915\u093e\u0930 \u0915\u093f\u092f\u093e \u091c\u093e\u090f \u0915\u093f \u092f\u0939 \u0915\u093f\u0938\u0940 \u092d\u0940 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 k<\/span> \u0915\u0947 \u0932\u093f\u090f \u0938\u0924\u094d\u092f \u0939\u0948, \u0924\u094b \u092f\u0939 \u0905\u0917\u0932\u0947 \u0915\u0947 \u0932\u093f\u090f \u092d\u0940 \u0938\u0924\u094d\u092f \u0939\u0948 S(k)<\/span>; \u0924\u094b \u0910\u0938\u093e \u0917\u0941\u0923 \u0938\u092d\u0940 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0932\u093f\u090f \u0938\u0924\u094d\u092f \u092e\u093e\u0928\u093e \u091c\u093e\u090f\u0917\u093e\u0964<\/em><\/p>\n\u092a\u094d\u0930\u0947\u0930\u0923\u093e \u0915\u093e \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u092e\u094c\u0932\u093f\u0915 \u0906\u0927\u093e\u0930 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u093e \u0939\u0948, \u092f\u0939 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u092a\u0930 \u0915\u093f\u0938\u0940 \u0917\u0941\u0923 \u0915\u094b \u0938\u093e\u092c\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0909\u092a\u092f\u094b\u0917\u0940 \u0909\u092a\u0915\u0930\u0923 \u092d\u0940 \u0939\u0948\u0964 \u0907\u0938\u0947 \u0926\u0947\u0916\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u091a\u0932\u093f\u090f \u090f\u0915 \u0938\u093e\u0927\u093e\u0930\u0923 \u0909\u0926\u093e\u0939\u0930\u0923 \u0926\u0947\u0916\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: justify;\">\n\u0909\u0926\u093e\u0939\u0930\u0923:<\/strong> \u092a\u094d\u0930\u0947\u0930\u0923\u093e \u0915\u0947 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0939\u092e \u092f\u0939 \u092a\u094d\u0930\u092e\u093e\u0923\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0905\u092a\u0928\u0947 \u0909\u0924\u094d\u0924\u0930\u093e\u0927\u093f\u0915\u093e\u0930\u0940 \u0938\u0947 \u092d\u093f\u0928\u094d\u0928 \u0939\u0948\u0964 <\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: justify; \">\n\u0939\u093e\u0932\u093e\u0902\u0915\u093f \u092f\u0939 \u090f\u0915 \u0938\u094d\u092a\u0937\u094d\u091f\u0924\u093e \u0939\u0948, \u092f\u0939 \u0924\u092c \u0938\u092e\u091d\u0928\u0947 \u092e\u0947\u0902 \u092e\u0926\u0926 \u0915\u0930\u0924\u093e \u0939\u0948 \u091c\u092c \u092a\u094d\u0930\u0947\u0930\u0923\u093e \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0938\u093e\u092c\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 <\/p>\n>\u092a\u094d\u0930\u092e\u093e\u0923:<\/strong><\/p>\n<ul>\n<li>\n\u092f\u0939 \u0938\u094d\u092a\u0937\u094d\u091f \u0939\u0948 \u0915\u093f 1<\/span> \u092d\u093f\u0928\u094d\u0928 \u0939\u0948 S(1)=2<\/span> \u0938\u0947\u0964 \u092f\u0939 \u0939\u0948 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u091a\u0930\u0923, <\/strong> \u091c\u0939\u093e\u0902 \u0939\u092e \u0938\u0924\u094d\u092f\u0924\u093e \u0915\u0940 \u092a\u0941\u0937\u094d\u091f\u093f \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0917\u0941\u0923 \u092a\u0939\u0932\u0947 \u0924\u0924\u094d\u0935 \u0915\u0947 \u0932\u093f\u090f \u0932\u093e\u0917\u0942 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 <\/p>\n<\/li>\n<li>\n\u092e\u093e\u0928 \u0932\u0947\u0902 \u0917\u0941\u0923 \u0915\u093f\u0938\u0940 k<\/span> \u0915\u0947 \u0932\u093f\u090f \u0932\u093e\u0917\u0942 \u0939\u094b\u0924\u093e \u0939\u0948, \u0905\u0930\u094d\u0925\u093e\u0924\u094d k\\neq S(k)<\/span>, \u091c\u094b \u0939\u092e \u0915\u0930\u0947\u0902\u0917\u0947 \u0935\u0939 \u092f\u0939 \u0939\u0948 \u0915\u093f \u0907\u0938\u0947 \u0938\u093e\u092c\u093f\u0924 \u0915\u0930\u0928\u093e \u0939\u0948 \u0915\u093f \u0907\u0938\u0938\u0947 \u092d\u0940 \u0938\u0924\u094d\u092f\u0924\u093e \u0915\u0940 \u092a\u0941\u0937\u094d\u091f\u093f \u0939\u094b\u0924\u0940 \u0939\u0948 S(k)<\/span> \u0915\u0947 \u0932\u093f\u090f (\u0905\u0930\u094d\u0925\u093e\u0924\u094d, \u092f\u0939 \u092d\u0940 \u0938\u0924\u094d\u092f \u0939\u0948 \u0915\u093f S(k)\\neq S(S(k))<\/span>. \u092f\u0939 \u0939\u0948 \u092a\u094d\u0930\u0947\u0930\u0923\u093e \u091a\u0930\u0923\u0964 <\/strong>\u0905\u0917\u0930 \u092f\u0947 \u0926\u094b \u091a\u0930\u0923 \u092a\u0942\u0930\u0947 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u092a\u094d\u0930\u0947\u0930\u0923\u093e \u092a\u0942\u0930\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948 \u0914\u0930 \u0917\u0941\u0923 \u0938\u092d\u0940 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0932\u093f\u090f \u0932\u093e\u0917\u0942 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 <\/p>\n[1]<\/strong> \u0936\u0941\u0930\u0942 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e \u0928\u094b\u091f \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f S(k) \\neq k,<\/span> \u0907\u0938\u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u0948 \u0915\u093f \\neg [k=S(k)]<\/span>.<\/p>\n[2]<\/strong> \u092a\u0930\u0902\u0924\u0941 \u091a\u0942\u0902\u0915\u093f k<\/span> \u0914\u0930 S(k)<\/span> \u0926\u094b\u0928\u094b\u0902 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0939\u0948\u0902, \u0905\u0915\u094d\u0937\u0930 2 \u0915\u0947 \u0924\u0939\u0924 \u0939\u092e \u0915\u0939 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0926\u094b\u0928\u094b\u0902 \u092e\u0947\u0902 \u0938\u0941\u0924\u0930\u093e \u0939\u0948: S(k)<\/span> \u0914\u0930 S(S(k))<\/span>, \u0915\u094d\u0930\u092e\u0936:\u0964 \u0926\u094b\u0928\u094b\u0902 \u092d\u0940 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0939\u0948\u0902\u0964<\/p>\n[3]<\/strong> \u092b\u093f\u0930, \u0905\u0915\u094d\u0937\u0930 4 \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u0939\u092e \u0915\u0939 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f: S(k) = S(S(k))<\/span> \u0938\u0942\u091a\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 \u0915\u093f k = S(k)<\/span>\u0964 \u0939\u092e \u0907\u0938\u0947 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0924\u0930\u0940\u0915\u0947 \u0938\u0947 \u0932\u093f\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n\\left[ S(k) = S(S(k)) \\right] \\rightarrow \\left[k = S(k)\\right]<\/span>\n\u091c\u094b \u0928\u093f\u0937\u0947\u0927 \u0915\u093e \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 \u0939\u0948, \u0915\u0939\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0938\u092e\u093e\u0928 \u0939\u0948 \u0915\u093f:<\/p>\n\\neg \\left[k = S(k)\\right] \\rightarrow \\neg \\left[ S(k) = S(S(k)) \\right] <\/span>\n[4]<\/strong> \u0905\u0902\u0924 \u092e\u0947\u0902, \u092a\u0942\u0930\u094d\u0935 \u092e\u0947\u0902 modus ponens \u0915\u094b \u0907\u0938 \u0905\u0902\u0924\u093f\u092e \u0935\u094d\u092f\u0915\u094d\u0924\u093f\u0924\u094d\u0935 \u0914\u0930 [1]<\/strong> \u092e\u0947\u0902 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u090f \u0917\u090f \u0935\u094d\u092f\u0915\u094d\u0924\u093f\u0924\u094d\u0935 \u0915\u0947 \u092c\u0940\u091a \u0915\u0930\u0924\u0947 \u0939\u0941\u090f \u0939\u092e \u092a\u093e\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f<\/p>\n\\neg \\left[ S(k) = S(S(k)) \\right] <\/span>\n\u091c\u094b \u0915\u0939\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0935\u0939\u0940 \u0939\u0948<\/p>\n S(k) \\neq S(S(k)) <\/span>\n\u0914\u0930 \u0907\u0938\u0932\u093f\u090f, \u0939\u092e\u0928\u0947 \u092a\u094d\u0930\u092e\u093e\u0923\u093f\u0924 \u0915\u093f\u092f\u093e \u0939\u0948 \u0915\u093f, \u092f\u0926\u093f S(k) \\neq k,<\/span> \u0938\u0924\u094d\u092f \u0939\u094b\u0924\u093e \u0939\u0948, \u0924\u094b S(k) \\neq S(S(k))<\/span> \u092d\u0940 \u0938\u0924\u094d\u092f \u0939\u094b\u0924\u093e \u0939\u0948; \u0914\u0930 \u092f\u0926\u093f 1\\neq 2<\/span> \u0938\u094d\u092a\u0937\u094d\u091f \u0939\u0948, \u0924\u094b \u092a\u094d\u0930\u0947\u0930\u0923\u093e \u092a\u0942\u0930\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948 \u0914\u0930 \u0932\u093f\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f<\/p>\n\\left(\\forall n\\in\\mathbb{N}\\right)\\left(n \\neq S(n)\\right) <\/span>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<a name=\"3\"><\/a><\/p>\n<h3>\u092a\u094d\u0930\u0926\u0930\u094d\u0936\u0928\u094b\u0902 \u092a\u0930 \u091f\u093f\u092a\u094d\u092a\u0923\u0940<\/h3>\n\u0939\u093e\u0932\u093e\u0902\u0915\u093f \u0909\u0926\u093e\u0939\u0930\u0923 \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0917\u0941\u0923 \u092c\u0939\u0941\u0924 \u0938\u094d\u092a\u0937\u094d\u091f \u0939\u0948, \u0917\u0923\u093f\u0924 \u092e\u0947\u0902 \u092f\u0939 \u0906\u092e \u0924\u094c\u0930 \u092a\u0930 \u0939\u094b\u0924\u093e \u0939\u0948 \u0915\u093f \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u0928 \u0907\u0938 \u0938\u094d\u092a\u0937\u094d\u091f\u0924\u093e \u0915\u094b \u092c\u0928\u093e\u090f \u0928\u0939\u0940\u0902 \u0930\u0916\u0924\u0947 \u0939\u0948\u0902\u0964 \u0939\u092e \u091c\u094b \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u0928 \u0926\u0947\u0916 \u091a\u0941\u0915\u0947 \u0939\u0948\u0902, \u0935\u0939 \u0909\u0926\u093e\u0939\u0930\u0923 \u0939\u0948 \u0915\u093f \u0906\u092e \u0924\u094c\u0930 \u092a\u0930 \u0917\u0923\u093f\u0924 \u092e\u0947\u0902 \u0915\u093e\u092e \u0915\u0930\u0924\u0947 \u0938\u092e\u092f \u0915\u094d\u092f\u093e \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0917\u0923\u093f\u0924 \u0915\u0940 \u0916\u093e\u0938\u0940\u092f\u0924 \u0915\u0947 \u0905\u0928\u0941\u092e\u093e\u0928 \u0924\u0915\u0928\u0940\u0915\u094b\u0902 \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u092e\u0947\u0902 \u092e\u0926\u0926 \u092a\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u092e\u0948\u0902 \u0906\u092a\u0915\u094b \u0938\u0941\u091d\u093e\u0935 \u0926\u0942\u0902\u0917\u093e \u0915\u093f \u0906\u092a <a href=\"http:\/\/toposuranos.com\/material\/hi\/category\/%e0%a4%97%e0%a4%a3%e0%a4%bf%e0%a4%a4\/%e0%a4%97%e0%a4%a3%e0%a4%bf%e0%a4%a4%e0%a5%80%e0%a4%af-%e0%a4%a4%e0%a4%b0%e0%a5%8d%e0%a4%95\/%e0%a4%aa%e0%a5%8d%e0%a4%b0%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%be%e0%a4%b5%e0%a4%a8%e0%a4%be-%e0%a4%a4%e0%a4%b0%e0%a5%8d%e0%a4%95\/\" target=\"_blank\" rel=\"noopener\">\u0917\u0923\u093f\u0924\u0940\u092f \u0924\u0930\u094d\u0915<\/strong><\/a> \u092a\u093e\u0920\u094d\u092f\u0915\u094d\u0930\u092e \u0915\u0947 \u0932\u093f\u090f \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0938\u093e\u092e\u0917\u094d\u0930\u0940 \u0915\u0940 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\u092a\u0930\u093f\u092d\u093e\u0937\u093e \u092a\u0930 \u091a\u0930\u094d\u091a\u093e \u0915\u0940 \u0917\u0908 \u0939\u0948: \u0915\u0941\u091b \u0917\u0923\u093f\u0924\u0940\u092f \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u091c\u094b \u0909\u0928\u0915\u0947 \u092e\u094c\u0932\u093f\u0915 \u0917\u0941\u0923\u094b\u0902 \u0915\u094b \u0938\u094d\u0925\u093f\u0930 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u092f\u0939 \u092d\u0940 \u092c\u0924\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0909\u0924\u094d\u0924\u0930\u093e\u0927\u093f\u0915\u093e\u0930\u093f\u092f\u094b\u0902 \u0915\u094b \u092a\u094d\u0930\u0924\u093f\u0937\u094d\u0920\u093f\u0924 \u0915\u0930\u0928\u0947 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