{"id":77274,"date":"2025-07-23T03:11:49","date_gmt":"2025-07-22T21:11:49","guid":{"rendered":"https:\/\/sarakhon.com\/?p=77274"},"modified":"2025-07-22T15:32:03","modified_gmt":"2025-07-22T09:32:03","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-239","status":"publish","type":"post","link":"https:\/\/sarakhon.com\/?p=77274","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\u09e9)"},"content":{"rendered":"<p><em>\u098f\u09a6\u09c7\u09b0 \u09af\u09cb\u0997\u09ab\u09b2 \u09a8\u09bf\u09b0\u09cd\u09a3\u09df \u0995\u09b0\u09a4\u09c7 \u09b8\u0995\u09cd\u09b7\u09ae\u0964 \u09aa\u09cd\u09b0\u09b8\u0999\u09cd\u0997\u09a4 \u09ac\u09b2\u09be \u09aa\u09cd\u09b0\u09df\u09cb\u099c\u09a8 \u098f\u0987 \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7 a = 1 \u09ac\u09b8\u09be\u09b2\u09c7 \u09aa\u09cd\u09b0\u09a5\u09ae \u0986\u09b0\u09cd\u09af\u09ad\u099f\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u099f\u09bf \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09ac\u09c7\u0964\u00a0<\/em><\/p>\n<p>\u0986\u09a7\u09c1\u09a8\u09bf\u0995 \u0997\u09a3\u09bf\u09a4\u09c7\u09b0 \u09ad\u09be\u09b7\u09be\u09df \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09b2\u09c7 \u09b9\u09ac\u09c7\u0964<\/p>\n<p>s 1 +s 2 &#8230;..+s<sub>a<\/sub>\u00a0 \u00a0= <img decoding=\"async\" class=\"alignnone wp-image-77275 \" src=\"https:\/\/sarakhon.com\/wp-content\/uploads\/2025\/07\/1-62-e1753175691195-300x52.jpg\" alt=\"\" width=\"173\" height=\"30\" srcset=\"https:\/\/sarakhon.com\/wp-content\/uploads\/2025\/07\/1-62-e1753175691195-300x52.jpg 300w, https:\/\/sarakhon.com\/wp-content\/uploads\/2025\/07\/1-62-e1753175691195.jpg 314w\" sizes=\"(max-width: 173px) 100vw, 173px\" \/><\/p>\n<p>\u098f\u0996\u09be\u09a8\u09c7 s,=( 1 + 2 +\u22c5\u22c5\u22c5\u22c5+r)<\/p>\n<p>\u0985\u09ac\u09b6\u09cd\u09af \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\u09b0 v = 2 5\/2 \u09b6\u09cd\u09b2\u09cb\u0995\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>s<sub>a<\/sub>+ s<sub>a<\/sub> + b +s<sub>a<\/sub>\u00a0+ 2b +\u22c5\u22c5\u22c5\u22c5+n \u09a4\u09ae \u09aa\u09a6<\/p>\n<p><img decoding=\"async\" class=\"alignnone  wp-image-77276\" src=\"https:\/\/sarakhon.com\/wp-content\/uploads\/2025\/07\/2-62-300x30.jpg\" alt=\"\" width=\"490\" height=\"49\" srcset=\"https:\/\/sarakhon.com\/wp-content\/uploads\/2025\/07\/2-62-300x30.jpg 300w, https:\/\/sarakhon.com\/wp-content\/uploads\/2025\/07\/2-62.jpg 589w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><\/p>\n<p>s<sub>a\u00a0<\/sub> = a + (a + b) +&#8230;..+\u00a0 \u00a0n\u00a0 \u09aa\u09a6 \u09aa\u09b0\u09cd\u09af\u09a8\u09cd\u09a4<\/p>\n<p>\u09ae\u09b9\u09be\u09ac\u09c0\u09b0 \u0985\u09ac\u09b6\u09cd\u09af \u09a8\u09bf\u09ae\u09cd\u09a8\u09cb\u0995\u09cd\u09a4 \u099a\u09be\u09b0 \u09a7\u09b0\u09a3\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09c0\u09b0 \u09af\u09cb\u0997\u09ab\u09b2\u09c7\u09b0 \u0989\u09b2\u09cd\u09b2\u09c7\u0996 \u0995\u09b0\u09c7\u099b\u09c7\u09a8<\/p>\n<p>(\u09e7) -\u09a4\u09ae \u09b8\u09cd\u09ac\u09be\u09ad\u09be\u09ac\u09bf\u0995 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09a6\u09bf\u09b0 \u09af\u09cb\u0997\u09ab\u09b2<br \/>\n(\u09e8) 1\u00b2 + 2\u00b2 +&#8230;+n\u00b2<br \/>\n(\u09e9) 1\u00b3 + 2\u00b3+&#8230;&#8230;.+n\u00b3<br \/>\n(\u09ea) \u098f\u09af\u09be\u09ae\u09c8\u0995\u09cd\u09af\u09be\u09a8\u09bf \u0985\u09b0\u09cd\u09a5\u09be\u09ce 1, 2,&#8230;&#8230;9<\/p>\n<p>\u098f\u09a6\u09c7\u09b0 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf 1, 3, 6, 10, 15, 21, 25, 36, 45<\/p>\n<p>\u098f\u09a6\u09c7\u09b0 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 1, 4, 10, 20, 35, 56, 84, 120, 165<\/p>\n<p>\u0986\u09b0\u09cd\u09af\u09ad\u099f (\u09ea\u09e9\u09ec \u0996\u09cd\u09b0\u09c0\u0983) \u0997\u09a3\u09bf\u09a4\u09aa\u09a6\u09c7\u09b0 \u09e8\u09e8-\u09a4\u09ae \u09b6\u09cd\u09b2\u09cb\u0995\u09c7 \u09af\u09be \u09ac\u09b2\u09c7\u099b\u09c7\u09a8 \u09a4\u09be\u09b0 \u09ae\u09b0\u09cd\u09ae\u09be\u09b0\u09cd\u09a5 \u09b9\u099a\u09cd\u099b\u09c7<\/p>\n<p>1\u00b2 +2\u00b2+3\u00b2 +&#8230;&#8230;+ n\u00b2 = (n(n + 1)(2n + 1))\/6<\/p>\n<p>\u098f\u09ac\u0982 1\u00b3+ 2\u00b3 + 3\u00b2 +&#8230;&#8230;+n\u00b2 =(1+2+3+&#8230;&#8230;+n)\u00b2<\/p>\n<p>3{ a\u00b2+ (2a)\u00b2 + (3a)\u00b2 +\u22c5\u22c5\u22c5+(na)\u00b2 } =(n+1)(na)\u00b2 +a{a+2a+\u22c5\u22c5\u22c5\u22c5 na}<\/p>\n<p>\u098f\u09ac\u0982 \u098f\u09a6\u09c7\u09b0 \u09af\u09cb\u0997\u09ab\u09b2 \u09a8\u09bf\u09b0\u09cd\u09a3\u09df \u0995\u09b0\u09a4\u09c7 \u09b8\u0995\u09cd\u09b7\u09ae\u0964 \u09aa\u09cd\u09b0\u09b8\u0999\u09cd\u0997\u09a4 \u09ac\u09b2\u09be \u09aa\u09cd\u09b0\u09df\u09cb\u099c\u09a8 \u098f\u0987 \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7 a = 1 \u09ac\u09b8\u09be\u09b2\u09c7 \u09aa\u09cd\u09b0\u09a5\u09ae \u0986\u09b0\u09cd\u09af\u09ad\u099f\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u099f\u09bf \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09ac\u09c7\u0964<\/p>\n<p><strong>(\u099a\u09b2\u09ac\u09c7)<\/strong><\/p>\n<h4 class=\"single-page-title\"><strong>\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\u09e8)<\/strong><\/h4>\n<blockquote class=\"wp-embedded-content\" data-secret=\"Hw0QNgvxiz\"><p><a href=\"https:\/\/sarakhon.com\/?p=77082\">\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\u09e8)<\/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\u09e8)&#8221; &#8212; Sarakhon \u0964 \u09b8\u09be\u09b0\u09be\u0995\u09cd\u09b7\u09a3\" src=\"https:\/\/sarakhon.com\/?p=77082&#038;embed=true#?secret=3Z5LzSIORt#?secret=Hw0QNgvxiz\" data-secret=\"Hw0QNgvxiz\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u098f\u09a6\u09c7\u09b0 \u09af\u09cb\u0997\u09ab\u09b2 \u09a8\u09bf\u09b0\u09cd\u09a3\u09df \u0995\u09b0\u09a4\u09c7 \u09b8\u0995\u09cd\u09b7\u09ae\u0964 \u09aa\u09cd\u09b0\u09b8\u0999\u09cd\u0997\u09a4 \u09ac\u09b2\u09be \u09aa\u09cd\u09b0\u09df\u09cb\u099c\u09a8 \u098f\u0987 \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7 a = 1 \u09ac\u09b8\u09be\u09b2\u09c7 \u09aa\u09cd\u09b0\u09a5\u09ae \u0986\u09b0\u09cd\u09af\u09ad\u099f\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u099f\u09bf \u09aa\u09be\u0993\u09df\u09be \u09af\u09be\u09ac\u09c7\u0964\u00a0 \u0986\u09a7\u09c1\u09a8\u09bf\u0995 \u0997\u09a3\u09bf\u09a4\u09c7\u09b0 \u09ad\u09be\u09b7\u09be\u09df \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09b2\u09c7 \u09b9\u09ac\u09c7\u0964 s 1 +s 2 &#8230;..+sa\u00a0 \u00a0= \u098f\u0996\u09be\u09a8\u09c7 s,=( 1 + 2 +\u22c5\u22c5\u22c5\u22c5+r) \u0985\u09ac\u09b6\u09cd\u09af \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\u09b0 v = 2 5\/2 \u09b6\u09cd\u09b2\u09cb\u0995\u09c7 \u09af\u09be \u09ac\u09b2\u09c7\u099b\u09c7\u09a8 \u09a4\u09be\u09b0 \u09ae\u09ae\u09be\u09b0\u09cd\u09a5 \u09b9\u099a\u09cd\u099b\u09c7 sa+ sa [&hellip;]<\/p>\n","protected":false},"author":5,"featured_media":77277,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[38,17],"tags":[],"location":[],"class_list":["post-77274","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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