{"id":77449,"date":"2025-07-24T03:30:22","date_gmt":"2025-07-23T21:30:22","guid":{"rendered":"https:\/\/sarakhon.com\/?p=77449"},"modified":"2025-07-23T15:49:34","modified_gmt":"2025-07-23T09:49:34","slug":"%e0%a6%aa%e0%a7%8d%e0%a6%b0%e0%a6%be%e0%a6%9a%e0%a7%80%e0%a6%a8-%e0%a6%ad%e0%a6%be%e0%a6%b0%e0%a6%a4%e0%a7%87-%e0%a6%97%e0%a6%a3%e0%a6%bf%e0%a6%a4%e0%a6%9a%e0%a6%b0%e0%a7%8d%e0%a6%9a%e0%a6%be-240","status":"publish","type":"post","link":"https:\/\/sarakhon.com\/?p=77449","title":{"rendered":"\u09aa\u09cd\u09b0\u09be\u099a\u09c0\u09a8 \u09ad\u09be\u09b0\u09a4\u09c7 \u0997\u09a3\u09bf\u09a4\u099a\u09b0\u09cd\u099a\u09be (\u09aa\u09b0\u09cd\u09ac-\u09e8\u09ea\u09ea)"},"content":{"rendered":"<p><em>\u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u0985\u09a8\u09cd\u09a4\u09b0 \u098f\u09ac\u0982 \u09aa\u09a6\u09b8\u0982\u0996\u09cd\u09af\u09be \u099c\u09be\u09a8\u09be \u09a5\u09be\u0995\u09b2\u09c7 \u09b6\u09c7\u09b7\u09aa\u09a6 \u0995\u09a4 \u09b8\u0982\u0996\u09cd\u09af\u09be, \u09ae\u09a7\u09cd\u09af\u09aa\u09a6 \u0995\u09a4 \u09b8\u0982\u0996\u09cd\u09af\u09be \u098f\u09ac\u0982 \u09af\u09c7 \u0995\u09cb\u09a8 \u09b8\u0982\u0996\u09cd\u09af\u0995 \u09aa\u09a6\u09c7\u09b0 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf \u09a8\u09bf\u09b0\u09cd\u09a3\u09df \u0995\u09b0\u09be \u09af\u09c7\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964<\/em><\/p>\n<p>\u0986\u09b0\u09cd\u09af\u09ad\u099f \u0985\u09ac\u09b6\u09cd\u09af 1\u00b3 +2\u00b3+&#8230;+ 10\u00b3 = (1\/2.10.11)\u00b2 \u09ac\u09b2\u09c7\u099b\u09c7\u09a8, \u09a4\u09ac\u09c7 \u0987\u099f\u09be\u09b2\u09c0\u09b0 \u09ac\u09bf\u0996\u09cd\u09af\u09be\u09a4 \u0997\u09a3\u09bf\u09a4\u09ac\u09bf\u09a6 \u09ab\u09bf\u09ac\u09cb\u09a8\u09be\u099a\u09cd\u099a\u09bf \u098f\u0995\u09be\u09a6\u09b6 \u09b6\u09a4\u09be\u09ac\u09cd\u09a6\u09c0\u09a4\u09c7 \u098f \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09c7 \u098f\u0995\u099f\u09bf \u09b8\u09b0\u09cd\u09ac\u099c\u09a8\u0997\u09cd\u09b0\u09be\u09b9\u09cd\u09af \u09b8\u09c2\u09a4\u09cd\u09b0 \u09a6\u09c7\u09a8\u0964 \u098f\u0987 \u09b8\u09c2\u09a4\u09cd\u09b0\u099f\u09bf \u09b9\u099a\u09cd\u099b\u09c7,<\/p>\n<p>1\u00b3 +2\u00b3+\u22c5\u22c5\u22c5\u22c5\u22c5+ n\u00b3 = {1\/2 n(n + 1)}\u00b2 \u09ae\u09b9\u09be\u09ac\u09c0\u09b0 \u0997\u09a3\u09bf\u09a4\u09b8\u09be\u09b0 \u09b8\u0982\u0997\u09cd\u09b0\u09b9\u09c7\u09b0 \u09af\u09b7\u09cd\u09a0 \u0985\u09a7\u09cd\u09af\u09be\u09df\u09c7 \u09af\u09be \u09ac\u09b2\u09c7\u099b\u09c7\u09a8 \u09a4\u09be\u09b0 \u09ae\u09ae\u09be\u09b0\u09cd\u09a5 \u09b9\u099a\u09cd\u099b\u09c7<\/p>\n<p>a\u00b2 + (a + b)\u00b2 + (a + 2b)\u00b2 +&#8230;..+n- \u09a4\u09ae \u09aa\u09a6<\/p>\n<p><img decoding=\"async\" class=\"size-medium wp-image-77450 aligncenter\" src=\"https:\/\/sarakhon.com\/wp-content\/uploads\/2025\/07\/7-46-300x39.jpg\" alt=\"\" width=\"300\" height=\"39\" srcset=\"https:\/\/sarakhon.com\/wp-content\/uploads\/2025\/07\/7-46-300x39.jpg 300w, https:\/\/sarakhon.com\/wp-content\/uploads\/2025\/07\/7-46.jpg 369w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>\u098f\u09ac\u0982 a\u00b3 + (a + b)\u00b3 + (a + 2b)\u00b3\u00a0+\u22c5\u22c5\u22c5\u22c5\u22c5\u22c5\u22c5+n- \u09a4\u09ae \u09aa\u09a6 \u09aa\u09b0\u09cd\u09af\u09a8\u09cd\u09a4<\/p>\n<p>= s\u00b2 b + sa(a &#8211; b)\u00a0 \u00a0\u09af\u09a6\u09bf a &gt; b \u09b9\u09df<\/p>\n<p>\u0985\u09a5\u09ac\u09be, s\u00b2 b &#8211; sa(a &#8211; b)\u00a0 \u09af\u09a6\u09bf a &lt; b \u09b9\u09df<\/p>\n<p>\u098f\u0996\u09be\u09a8\u09c7 s= a + (a + b) + (a + 2b) +\u22c5\u22c5\u22c5\u22c5\u22c5+n \u09a4\u09ae \u09aa\u09a6 \u09aa\u09b0\u09cd\u09af\u09a8\u09cd\u09a4<\/p>\n<p>\u09aa\u09cd\u09b0\u09a5\u09ae \u0986\u09b0\u09cd\u09af\u09ad\u099f, \u09ae\u09b9\u09be\u09ac\u09c0\u09b0, \u09aa\u09cd\u09b0\u09ae\u09c1\u0996\u09c7\u09b0\u09be \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09c0 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09c7 \u09af\u09be \u0989\u09b2\u09cd\u09b2\u09c7\u0996 \u0995\u09b0\u09c7\u099b\u09c7\u09a8 \u09a4\u09be\u09b0 \u099a\u09c7\u09df\u09c7 \u0985\u09a8\u09c7\u0995 \u09b8\u09c1\u09b6\u09c3\u0999\u09cd\u0996\u09b2\u09ad\u09be\u09ac\u09c7 \u09ac\u09cd\u09b0\u09b9\u09cd\u09ae\u0997\u09c1\u09aa\u09cd\u09a4 \u098f\u09ac\u0982 \u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09df \u09ad\u09be\u09b8\u09cd\u0995\u09b0\u09be\u099a\u09be\u09b0\u09cd\u09af \u0986\u09b2\u09cb\u099a\u09a8\u09be \u0995\u09b0\u09c7\u099b\u09c7\u09a8\u0964 a &lt; b<\/p>\n<p>\u09ac\u09cd\u09b0\u09b9\u09cd\u09ae\u0997\u09c1\u09aa\u09cd\u09a4 \u09ac\u09cd\u09b0\u09be\u09b9\u09cd\u09ae\u09b8\u09cd\u09ab\u09c1\u099f \u09b8\u09bf\u09a6\u09cd\u09a7\u09be\u09a8\u09cd\u09a4\u09c7\u09b0 \u0997\u09a3\u09bf\u09a4\u09be\u09a7\u09cd\u09af\u09be\u09df\u09c7\u09b0 \u09e7\u09ed \u09a8\u0982 \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7 \u09ac\u09b2\u09c7\u099b\u09c7\u09a8 &#8220;\u09aa\u09a6\u09ae\u09c7\u0995\u09b9\u09c0\u09a8\u09ae\u09c1\u09a4\u09cd\u09a4\u09b0\u0997\u09c1\u09a3\u09bf\u09a4\u0982 \u09b8\u0982\u09af\u09c1\u0995\u09cd\u09a4\u09ae\u09be\u09a6\u09bf\u09a8\u09be \u09b9\u09b8\u09cd\u09a4\u09cd\u09af\u09a7\u09a8\u09ae\u09cd\u0964 \u0986\u09a6\u09bf\u09af\u09c1\u09a4\u09be\u09a8\u09cd\u09a4\u09cd\u09af\u09a7\u09a8\u09be\u09b0\u09cd\u09a7\u0982 \u09ae\u09a7\u09cd\u09af\u09a7\u09a8\u0982 \u09aa\u09a6\u0997\u09c1\u09a3\u09a8\u0982 \u0997\u09a3\u09bf\u09a4\u09ae\u09cd\u0964<\/p>\n<p>\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09aa\u09cd\u09b0\u09a5\u09ae\u09aa\u09a6, \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u0985\u09a8\u09cd\u09a4\u09b0 \u098f\u09ac\u0982 \u09aa\u09a6\u09b8\u0982\u0996\u09cd\u09af\u09be \u099c\u09be\u09a8\u09be \u09a5\u09be\u0995\u09b2\u09c7 \u09b6\u09c7\u09b7\u09aa\u09a6 \u0995\u09a4 \u09b8\u0982\u0996\u09cd\u09af\u09be, \u09ae\u09a7\u09cd\u09af\u09aa\u09a6 \u0995\u09a4 \u09b8\u0982\u0996\u09cd\u09af\u09be \u098f\u09ac\u0982 \u09af\u09c7 \u0995\u09cb\u09a8 \u09b8\u0982\u0996\u09cd\u09af\u0995 \u09aa\u09a6\u09c7\u09b0 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf \u09a8\u09bf\u09b0\u09cd\u09a3\u09df \u0995\u09b0\u09be \u09af\u09c7\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964 \u09aa\u09a6\u09b8\u0982\u0996\u09cd\u09af\u09be \u09a5\u09c7\u0995\u09c7 \u098f\u0995 \u09ac\u09bf\u09df\u09cb\u0997 \u0995\u09b0\u09c7 \u0990 \u09ac\u09bf\u09df\u09cb\u0997\u09ab\u09b2\u0995\u09c7 \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u0985\u09a8\u09cd\u09a4\u09b0 \u09a6\u09bf\u09df\u09c7 \u0997\u09c1\u09a3 \u0995\u09b0\u09c7 \u09a4\u09be\u09b0\u09aa\u09b0 \u09aa\u09cd\u09b0\u09a5\u09ae \u09aa\u09a6 \u09af\u09cb\u0997 \u0995\u09b0\u09b2\u09c7 \u09b6\u09c7\u09b7 \u09aa\u09a6 \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09ac\u09c7\u0964 \u098f\u0987 \u09b6\u09c7\u09b7\u09aa\u09a6\u09c7\u09b0 \u09b8\u0999\u09cd\u0997\u09c7 \u09aa\u09cd\u09b0\u09a5\u09ae \u09aa\u09a6 \u0986\u09ac\u09be\u09b0 \u09af\u09cb\u0997 \u09a6\u09bf\u09df\u09c7 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srcset=\"https:\/\/sarakhon.com\/wp-content\/uploads\/2025\/07\/8-47-300x50.jpg 300w, https:\/\/sarakhon.com\/wp-content\/uploads\/2025\/07\/8-47.jpg 451w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>\u098f\u0996\u09be\u09a8\u09c7 -\u09a4\u09ae \u09aa\u09a6, \u098f \u09aa\u09cd\u09b0\u09a5\u09ae \u09aa\u09a6, \u09ee \u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u0985\u09a8\u09cd\u09a4\u09b0, \u09ae\u09a7\u09cd\u09af\u09ae \u09aa\u09a6\u0964 S\u09b8\u0982\u0996\u09cd\u09af\u0995 \u09aa\u09a6\u09c7\u09b0 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf\u0964<\/p>\n<p>\u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09df \u09ad\u09be\u09b8\u09cd\u0995\u09b0\u09be\u099a\u09be\u09b0\u09cd\u09af \u09ac\u09b2\u09c7\u099b\u09c7\u09a8:<\/p>\n<p>\u09af\u09a5\u09cb\u09a4\u09cd\u09a4\u09b0\u099a\u09df\u09c7\u09b9\u09b8\u09cd\u09a4\u09cd\u09af\u09be\u09a6\u09bf\u09a7\u09a8\u099c\u09cd\u099e\u09be\u09a8\u09be\u09df \u0995\u09b0\u09a3\u09b8\u09c2\u09a4\u09cd\u09b0\u0982 \u09ac\u09c3\u09a4\u09cd\u09a4\u09ae\u09cd\u0964 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\u09aa\u09be\u0981\u099a\u099f\u09bf \u0995\u09b0\u09c7 \u09ac\u09cd\u09b0\u09b9\u09cd\u09ae \u09ac\u09c7\u09b6\u09c0 \u09a6\u09bf\u09a4\u09c7 \u09a5\u09be\u0995\u09c7 \u09a4\u09be\u09b9\u09b2\u09c7 \u098f\u0995\u09aa\u0995\u09cd\u09b7 \u09a6\u09bf\u09a8\u0995\u09be\u09b2\u09c7 \u0990 \u09b2\u09cb\u0995 \u0995\u09a4 \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u09a6\u09be\u09a8 \u0995\u09b0\u09c7\u099b\u09bf\u09b2?<\/p>\n<p><strong>(\u099a\u09b2\u09ac\u09c7)<\/strong><\/p>\n<h4 class=\"single-page-title\">\u09aa\u09cd\u09b0\u09be\u099a\u09c0\u09a8 \u09ad\u09be\u09b0\u09a4\u09c7 \u0997\u09a3\u09bf\u09a4\u099a\u09b0\u09cd\u099a\u09be (\u09aa\u09b0\u09cd\u09ac-\u09e8\u09ea\u09e9)<\/h4>\n<blockquote class=\"wp-embedded-content\" data-secret=\"xxXdoLAxzb\"><p><a href=\"https:\/\/sarakhon.com\/?p=77274\">\u09aa\u09cd\u09b0\u09be\u099a\u09c0\u09a8 \u09ad\u09be\u09b0\u09a4\u09c7 \u0997\u09a3\u09bf\u09a4\u099a\u09b0\u09cd\u099a\u09be (\u09aa\u09b0\u09cd\u09ac-\u09e8\u09ea\u09e9)<\/a><\/p><\/blockquote>\n<p><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"&#8220;\u09aa\u09cd\u09b0\u09be\u099a\u09c0\u09a8 \u09ad\u09be\u09b0\u09a4\u09c7 \u0997\u09a3\u09bf\u09a4\u099a\u09b0\u09cd\u099a\u09be (\u09aa\u09b0\u09cd\u09ac-\u09e8\u09ea\u09e9)&#8221; &#8212; Sarakhon \u0964 \u09b8\u09be\u09b0\u09be\u0995\u09cd\u09b7\u09a3\" src=\"https:\/\/sarakhon.com\/?p=77274&#038;embed=true#?secret=X27O0VBTya#?secret=xxXdoLAxzb\" data-secret=\"xxXdoLAxzb\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u09b8\u09be\u09a7\u09be\u09b0\u09a3 \u0985\u09a8\u09cd\u09a4\u09b0 \u098f\u09ac\u0982 \u09aa\u09a6\u09b8\u0982\u0996\u09cd\u09af\u09be \u099c\u09be\u09a8\u09be \u09a5\u09be\u0995\u09b2\u09c7 \u09b6\u09c7\u09b7\u09aa\u09a6 \u0995\u09a4 \u09b8\u0982\u0996\u09cd\u09af\u09be, \u09ae\u09a7\u09cd\u09af\u09aa\u09a6 \u0995\u09a4 \u09b8\u0982\u0996\u09cd\u09af\u09be \u098f\u09ac\u0982 \u09af\u09c7 \u0995\u09cb\u09a8 \u09b8\u0982\u0996\u09cd\u09af\u0995 \u09aa\u09a6\u09c7\u09b0 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf \u09a8\u09bf\u09b0\u09cd\u09a3\u09df \u0995\u09b0\u09be \u09af\u09c7\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964 \u0986\u09b0\u09cd\u09af\u09ad\u099f \u0985\u09ac\u09b6\u09cd\u09af 1\u00b3 +2\u00b3+&#8230;+ 10\u00b3 = (1\/2.10.11)\u00b2 \u09ac\u09b2\u09c7\u099b\u09c7\u09a8, \u09a4\u09ac\u09c7 \u0987\u099f\u09be\u09b2\u09c0\u09b0 \u09ac\u09bf\u0996\u09cd\u09af\u09be\u09a4 \u0997\u09a3\u09bf\u09a4\u09ac\u09bf\u09a6 \u09ab\u09bf\u09ac\u09cb\u09a8\u09be\u099a\u09cd\u099a\u09bf \u098f\u0995\u09be\u09a6\u09b6 \u09b6\u09a4\u09be\u09ac\u09cd\u09a6\u09c0\u09a4\u09c7 \u098f \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09c7 \u098f\u0995\u099f\u09bf \u09b8\u09b0\u09cd\u09ac\u099c\u09a8\u0997\u09cd\u09b0\u09be\u09b9\u09cd\u09af \u09b8\u09c2\u09a4\u09cd\u09b0 \u09a6\u09c7\u09a8\u0964 \u098f\u0987 \u09b8\u09c2\u09a4\u09cd\u09b0\u099f\u09bf \u09b9\u099a\u09cd\u099b\u09c7, 1\u00b3 +2\u00b3+\u22c5\u22c5\u22c5\u22c5\u22c5+ n\u00b3 = {1\/2 n(n + 1)}\u00b2 \u09ae\u09b9\u09be\u09ac\u09c0\u09b0 [&hellip;]<\/p>\n","protected":false},"author":5,"featured_media":77452,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[38,17],"tags":[],"location":[],"class_list":["post-77449","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-38","category-17"],"cmb2":{"heading_information":{"sub_title":""},"reporter_information":{"video":"","reporter_name":"\u09aa\u09cd\u09b0\u09a6\u09c0\u09aa \u0995\u09c1\u09ae\u09be\u09b0 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