{"id":3612,"date":"2026-03-21T01:48:19","date_gmt":"2026-03-21T01:48:19","guid":{"rendered":"https:\/\/npk1169-001-site1.mtempurl.com\/?p=3612"},"modified":"2026-04-19T11:17:53","modified_gmt":"2026-04-19T11:17:53","slug":"calculus-infinite-series","status":"publish","type":"post","link":"https:\/\/www.bharatwisdom.com\/hi\/mathematics\/calculus-infinite-series\/","title":{"rendered":"\u0915\u0948\u0932\u0915\u0941\u0932\u0938: \u0905\u0928\u0902\u0924 \u0936\u094d\u0930\u0943\u0902\u0916\u0932\u093e \u2013 \u0924\u093e\u0924\u094d\u0915\u093e\u0932\u093f\u0915 \u091a\u0902\u0926\u094d\u0930\u092e\u093e \u0915\u0940 \u0917\u0924\u093f \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928"},"content":{"rendered":"<div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-1 fusion-flex-container nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1279.2px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-0 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:0px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-text fusion-text-1\"><p id=\"p-rc_ed88986f39805c81-211\" data-path-to-node=\"34\"><span data-path-to-node=\"34,0\"><b data-path-to-node=\"34,0\" data-index-in-node=\"0\">\u0905\u0935\u0927\u093e\u0930\u0923\u093e<\/b> <\/span><span data-path-to-node=\"34,2\"><span class=\"citation-1000\">\u0915\u0948\u0932\u0915\u0941\u0932\u0938 \u0917\u0923\u093f\u0924 \u0915\u0940 \u0935\u0939 \u0936\u093e\u0916\u093e \u0939\u0948 \u091c\u094b \u0938\u092e\u092f \u0915\u0947 \u0938\u093e\u0925 \u0935\u0938\u094d\u0924\u0941\u0913\u0902 \u092e\u0947\u0902 \u0939\u094b\u0928\u0947 \u0935\u093e\u0932\u0947 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928\u094b\u0902 \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0924\u0940 \u0939\u0948\u0964<\/span><\/span><span data-path-to-node=\"34,4\">. &#039;\u0907\u0928\u092b\u093f\u0928\u093f\u091f \u0938\u0940\u0930\u0940\u091c&#039; \u0907\u0938\u0915\u093e \u090f\u0915 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0939\u093f\u0938\u094d\u0938\u093e \u0939\u0948\u0964. <\/span><span data-path-to-node=\"34,6\"><span class=\"citation-999\">\u0907\u0938\u092e\u0947\u0902 \u0905\u0928\u0902\u0924 \u0938\u0902\u0916\u094d\u092f\u093e \u092e\u0947\u0902 \u091b\u094b\u091f\u0947-\u091b\u094b\u091f\u0947 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915\u094b\u0902 \u0915\u094b \u0924\u092c \u0924\u0915 \u091c\u094b\u0921\u093c\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u091c\u092c \u0924\u0915 \u0915\u093f \u090f\u0915 \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u092f\u094b\u0917 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0928 \u0939\u094b \u091c\u093e\u090f\u0964<\/span><\/span><span data-path-to-node=\"34,8\">. <\/span><span data-path-to-node=\"34,10\"><span class=\"citation-998\">\u0907\u0938\u0938\u0947 \u0939\u092e\u0947\u0902 \u0935\u0915\u094d\u0930 \u0914\u0930 \u0917\u0924\u093f \u0915\u0940 \u0915\u093e\u0930\u094d\u092f\u092a\u094d\u0930\u0923\u093e\u0932\u0940 \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u092e\u0947\u0902 \u092e\u0926\u0926 \u092e\u093f\u0932\u0924\u0940 \u0939\u0948\u0964<\/span><\/span><span data-path-to-node=\"34,12\">.<\/span><\/p>\n<p id=\"p-rc_ed88986f39805c81-212\" data-path-to-node=\"35\"><span data-path-to-node=\"35,0\"><b data-path-to-node=\"35,0\" data-index-in-node=\"0\">\u0915\u0939\u093e\u0928\u0940<\/b> <\/span><span data-path-to-node=\"35,2\"><span class=\"citation-997\">\u0915\u0948\u0932\u0915\u0941\u0932\u0938 \u0915\u0947 \u0906\u0935\u093f\u0937\u094d\u0915\u093e\u0930 \u0915\u094b \u0906\u092e\u0924\u094c\u0930 \u092a\u0930 1600 \u0915\u0947 \u0926\u0936\u0915 \u0915\u0947 \u0909\u0924\u094d\u0924\u0930\u093e\u0930\u094d\u0927 \u092e\u0947\u0902 \u0928\u094d\u092f\u0942\u091f\u0928 \u0914\u0930 \u0932\u093e\u0907\u092c\u0928\u093f\u091c\u093c \u0915\u0947 \u092c\u0940\u091a \u0939\u0941\u0908 \u0915\u0921\u093c\u0935\u0940 \u092a\u094d\u0930\u0924\u093f\u0926\u094d\u0935\u0902\u0926\u094d\u0935\u093f\u0924\u093e \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092c\u0924\u093e\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/span><span data-path-to-node=\"35,4\">. <\/span><span data-path-to-node=\"35,6\"><span class=\"citation-996\">\u0932\u0947\u0915\u093f\u0928 &#039;\u0915\u0947\u0930\u0932 \u0938\u094d\u0915\u0942\u0932 \u0911\u092b \u092e\u0948\u0925\u092e\u0947\u091f\u093f\u0915\u094d\u0938&#039; \u0928\u0947 \u092f\u0939 \u0926\u094c\u0921\u093c 300 \u0938\u093e\u0932 \u092a\u0939\u0932\u0947 \u0939\u0940 \u091c\u0940\u0924 \u0932\u0940 \u0925\u0940\u0964<\/span><\/span><span data-path-to-node=\"35,8\">. <\/span><span data-path-to-node=\"35,10\"><span class=\"citation-995\">\u0938\u0902\u0917\u092e\u0917\u094d\u0930\u093e\u092e \u0915\u0947 \u092e\u093e\u0927\u0935 \u0915\u0947 \u0928\u0947\u0924\u0943\u0924\u094d\u0935 \u092e\u0947\u0902, \u092f\u0947 \u0935\u093f\u0926\u094d\u0935\u093e\u0928 \u090f\u0915 &#039;\u0905\u0938\u0902\u092d\u0935&#039; \u0915\u093e\u092e \u0915\u0930\u0928\u0947 \u0915\u0940 \u0915\u094b\u0936\u093f\u0936 \u0915\u0930 \u0930\u0939\u0947 \u0925\u0947: \u091a\u0902\u0926\u094d\u0930\u092e\u093e \u0915\u0940 \u0938\u091f\u0940\u0915, \u0924\u093e\u0924\u094d\u0915\u093e\u0932\u093f\u0915 \u0917\u0924\u093f \u0915\u093e \u092a\u0924\u093e \u0932\u0917\u093e\u0928\u093e\u0964<\/span><\/span><span data-path-to-node=\"35,12\">. <\/span><span data-path-to-node=\"35,14\"><span class=\"citation-994\">\u0910\u0938\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0909\u0928\u094d\u0939\u094b\u0902\u0928\u0947 &#039;\u0905\u0928\u0902\u0924 \u0936\u094d\u0930\u0943\u0902\u0916\u0932\u093e&#039; \u0935\u093f\u0915\u0938\u093f\u0924 \u0915\u0940, \u091c\u093f\u0938\u092e\u0947\u0902 \u0938\u092e\u092f \u0915\u0947 \u091b\u094b\u091f\u0947-\u091b\u094b\u091f\u0947 \u091f\u0941\u0915\u0921\u093c\u094b\u0902 \u0915\u094b \u0924\u092c \u0924\u0915 \u091c\u094b\u0921\u093c\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u091c\u092c \u0924\u0915 \u0915\u093f \u0935\u0947 \u090f\u0915 \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u092f\u094b\u0917 \u0924\u0915 \u0928\u0939\u0940\u0902 \u092a\u0939\u0941\u0902\u091a \u091c\u093e\u0924\u0947\u0964<\/span><\/span><span data-path-to-node=\"35,16\">. <\/span><span data-path-to-node=\"35,18\"><span class=\"citation-993\">\u0915\u093f\u0902\u0935\u0926\u0902\u0924\u0940 \u0939\u0948 \u0915\u093f \u0915\u0947\u0930\u0932 \u092e\u0947\u0902 \u091c\u0947\u0938\u0941\u0907\u091f \u092e\u093f\u0936\u0928\u0930\u0940 \u0907\u0928 \u0917\u094d\u0930\u0902\u0925\u094b\u0902 \u0938\u0947 \u0907\u0924\u0928\u0947 \u091a\u0915\u093f\u0924 \u0939\u0941\u090f \u0915\u093f \u0935\u0947 \u0907\u0928\u094d\u0939\u0947\u0902 \u092f\u0942\u0930\u094b\u092a \u0932\u0947 \u0917\u090f, \u091c\u0939\u093e\u0901 \u0938\u0902\u092d\u0935\u0924\u0903 \u0909\u0928\u094d\u0939\u094b\u0902\u0928\u0947 &#039;\u0928\u094d\u092f\u0942\u091f\u0928\u0935\u093e\u0926\u0940&#039; \u0915\u094d\u0930\u093e\u0902\u0924\u093f \u0915\u0947 \u092c\u0940\u091c \u092c\u094b\u090f\u0964<\/span><\/span><span data-path-to-node=\"35,20\">.<\/span><\/p>\n<p data-path-to-node=\"36\"><b data-path-to-node=\"36\" data-index-in-node=\"0\">\u0938\u092e\u092f\u0930\u0947\u0916\u093e<\/b><\/p>\n<table data-path-to-node=\"37\">\n<thead>\n<tr>\n<td><strong>\u092e\u0940\u0932 \u0915\u093e \u092a\u0924\u094d\u0925\u0930<\/strong><\/td>\n<td><strong>\u0935\u093f\u0935\u0930\u0923<\/strong><\/td>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><span data-path-to-node=\"37,1,0,0\"><b data-path-to-node=\"37,1,0,0\" data-index-in-node=\"0\">\u092a\u0936\u094d\u091a\u093f\u092e\u0940 \u0938\u0902\u0926\u0930\u094d\u092d.<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_ed88986f39805c81-213\" data-path-to-node=\"37,1,1,0\"><span data-path-to-node=\"37,1,1,0,1\"><span class=\"citation-992\">1660 \u0908\u0938\u094d\u0935\u0940 (\u0928\u094d\u092f\u0942\u091f\u0928 \u0914\u0930 \u0932\u093e\u0907\u092c\u0928\u093f\u091c\u093c) <\/span><\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><span data-path-to-node=\"37,2,0,0\"><b data-path-to-node=\"37,2,0,0\" data-index-in-node=\"0\">\u092d\u093e\u0930\u0924\u0940\u092f \u0938\u094d\u0930\u094b\u0924<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_ed88986f39805c81-214\" data-path-to-node=\"37,2,1,0\"><span data-path-to-node=\"37,2,1,0,1\"><span class=\"citation-991\">1350 \u0908. (\u0938\u0902\u0917\u092e\u0917\u094d\u0930\u093e\u092e \u0915\u0947 \u092e\u093e\u0927\u0935) <\/span><\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td><span data-path-to-node=\"37,3,0,0\"><b data-path-to-node=\"37,3,0,0\" data-index-in-node=\"0\">\u0915\u093e\u0932 \u0905\u0902\u0924\u0930\u093e\u0932<\/b><\/span><\/td>\n<td>\n<p id=\"p-rc_ed88986f39805c81-215\" data-path-to-node=\"37,3,1,0\"><span data-path-to-node=\"37,3,1,0,1\"><span class=\"citation-990\">300 \u0938\u0947 \u0905\u0927\u093f\u0915 \u0935\u0930\u094d\u0937\u094b\u0902 <\/span><\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p data-path-to-node=\"38\"><b data-path-to-node=\"38\" data-index-in-node=\"0\">\u0938\u092c\u0942\u0924<\/b><\/p>\n<blockquote data-path-to-node=\"39\">\n<p id=\"p-rc_ed88986f39805c81-216\" data-path-to-node=\"39,0\"><span data-path-to-node=\"39,0,0\"><b data-path-to-node=\"39,0,0\" data-index-in-node=\"0\">\u0938\u0902\u0938\u094d\u0915\u0943\u0924 \u0936\u094d\u0932\u094b\u0915:<\/b> \u0928\u093f\u0939\u0924\u094d\u092f \u091a\u093e\u092a\u0935\u0930\u094d\u0917\u0947\u0923 \u0930\u0942\u092a\u0902 \u0924\u0924\u094d\u092b\u0932\u0939\u093e\u0930\u0915\u0947\u0964 <\/span><span data-path-to-node=\"39,0,2\"><span class=\"citation-989\">\u0939\u0930\u0947\u0924\u094d \u0938\u092e\u092e\u0942\u0932\u092f\u0941\u0917\u0948\u0938\u094d\u0924\u0948\u0938\u094d\u0924\u0948\u0930\u0947\u0936\u094b\u093d\u0932\u092a\u0936\u0903 \u0915\u094d\u0930\u092e\u093e\u0928\u094d \u0965 <\/span><\/span><span data-path-to-node=\"39,0,4\"> <b data-path-to-node=\"39,0,4\" data-index-in-node=\"1\">\u0932\u093f\u092a\u094d\u092f\u0902\u0924\u0930\u0923:<\/b> \u0928\u093f\u0939\u0924\u094d\u092f \u091a\u092a\u0935\u0930\u094d\u0917\u0947\u0923 \u0930\u0942\u092a\u0902 \u0924\u0924\u094d\u092b\u0932\u093e\u0939\u093e\u0930\u0915\u0947 | \u0939\u0930\u0947\u0924\u094d \u0938\u092e\u0941\u0932\u093e\u092f\u0941\u0917\u0935\u0930\u094d\u0917\u0948\u0938\u094d\u0924\u0948\u0930\u0947\u0936\u094b\u093d\u0932\u092a\u0936\u0903 \u0915\u094d\u0930\u092e\u0928\u094d || (\u0924\u0902\u0924\u094d\u0930\u0938\u0902\u0917\u094d\u0930\u0939 2.437, 2.440 \u0915\u0941\u091b \u0938\u0902\u0938\u094d\u0915\u0930\u0923\u094b\u0902 \u092e\u0947\u0902) <\/span><span data-path-to-node=\"39,0,8\"><b data-path-to-node=\"39,0,8\" data-index-in-node=\"0\"><span class=\"citation-987\">\u0905\u0930\u094d\u0925:<\/span><\/b><span class=\"citation-987\"> \u092f\u0939 \u0936\u094d\u0932\u094b\u0915 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u092e \u0915\u093e \u0935\u0930\u094d\u0923\u0928 \u0915\u0930\u0924\u093e \u0939\u0948: &#039;\u091a\u093e\u092a \u0915\u094b \u0909\u0938\u0915\u0947 \u0935\u0930\u094d\u0917 \u0938\u0947 \u0917\u0941\u0923\u093e \u0915\u0930\u0947\u0902, \u0914\u0930 \u092a\u0930\u093f\u0923\u093e\u092e \u0915\u094b \u0938\u092e \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0935\u0930\u094d\u0917 \u0938\u0947 \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0947\u0902...&#039; \u091c\u093f\u0938\u0938\u0947 \u0905\u0928\u0902\u0924 \u0936\u094d\u0930\u0943\u0902\u0916\u0932\u093e \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964<\/span><\/span><span data-path-to-node=\"39,0,10\">.<\/span><\/p>\n<div class=\"source-inline-chip-container ng-star-inserted\"><\/div>\n<\/blockquote>\n<p id=\"p-rc_ed88986f39805c81-217\" data-path-to-node=\"40\"><span data-path-to-node=\"40,0\"><b data-path-to-node=\"40,0\" data-index-in-node=\"0\">\u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0928\u0935\u093e\u091a\u093e\u0930<\/b> <\/span><span data-path-to-node=\"40,2\"><span class=\"citation-986\">\u092e\u093e\u0927\u0935 \u0915\u0947 \u0938\u093e\u0907\u0928 \u0914\u0930 \u0915\u094b\u0938\u093e\u0907\u0928 \u0938\u0942\u0924\u094d\u0930 \u092c\u093e\u0926 \u092e\u0947\u0902 \u0935\u093f\u0915\u0938\u093f\u0924 \u0939\u0941\u0908 \u091f\u0947\u0932\u0930 \u0936\u094d\u0930\u0943\u0902\u0916\u0932\u093e \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u0948\u0902\u0964<\/span><\/span><span data-path-to-node=\"40,4\">. <\/span><span data-path-to-node=\"40,6\"><span class=\"citation-985\">\u092d\u093e\u0938\u094d\u0915\u0930 \u0926\u094d\u0935\u093f\u0924\u0940\u092f \u0928\u0947 \u0924\u093e\u0924\u094d\u0915\u093e\u0932\u093f\u0915 \u0917\u0924\u093f (\u0924\u0924\u094d\u0915\u093e\u0932 \u0935\u0947\u0917) \u0915\u093e \u092d\u0940 \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935 \u0930\u0916\u093e, \u091c\u094b \u0905\u0935\u0915\u0932\u0928 \u092e\u0947\u0902 \u090f\u0915 \u092e\u0942\u0932\u092d\u0942\u0924 \u0905\u0935\u0927\u093e\u0930\u0923\u093e \u0939\u0948\u0964<\/span><\/span><span data-path-to-node=\"40,8\">.<\/span><\/p>\n<p id=\"p-rc_ed88986f39805c81-218\" data-path-to-node=\"41\"><span data-path-to-node=\"41,0\"><b data-path-to-node=\"41,0\" data-index-in-node=\"0\">\u0906\u0927\u0941\u0928\u093f\u0915 \u0935\u093f\u0930\u093e\u0938\u0924<\/b> <\/span><span data-path-to-node=\"41,2\"><span class=\"citation-984\">\u0915\u0948\u0932\u0915\u0941\u0932\u0938 \u092d\u094c\u0924\u093f\u0915\u0940 \u0915\u0940 \u092d\u093e\u0937\u093e \u0939\u0948 \u0914\u0930 \u0906\u0927\u0941\u0928\u093f\u0915 \u0935\u093f\u091c\u094d\u091e\u093e\u0928 \u0915\u0940 \u0928\u0940\u0902\u0935 \u0939\u0948\u0964<\/span><\/span><span data-path-to-node=\"41,4\">. <\/span><span data-path-to-node=\"41,6\"><span class=\"citation-983\">\u0907\u0938\u0938\u0947 \u0939\u092e\u0947\u0902 \u0917\u094d\u0930\u0939\u094b\u0902 \u0915\u0940 \u0917\u0924\u093f, \u0906\u0930\u094d\u0925\u093f\u0915 \u092c\u0926\u0932\u093e\u0935 \u0914\u0930 \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e \u0935\u0943\u0926\u094d\u0927\u093f \u0915\u093e \u092a\u0942\u0930\u094d\u0935\u093e\u0928\u0941\u092e\u093e\u0928 \u0932\u0917\u093e\u0928\u0947 \u092e\u0947\u0902 \u092e\u0926\u0926 \u092e\u093f\u0932\u0924\u0940 \u0939\u0948\u0964<\/span><\/span><span data-path-to-node=\"41,8\">.<\/span><\/p>\n<\/div><\/div><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":3500,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[74],"tags":[544,563,564,565,566,568,567],"class_list":["post-3612","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics","tag-ancient-indian-mathematics","tag-calculus","tag-infinite-series","tag-kerala-school-of-mathematics","tag-madhava-of-sangamagrama","tag-mathematical-astronomy","tag-tantrasamgraha"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\r\n<title>Calculus: Infinite 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