{"id":78200,"date":"2025-07-29T03:58:44","date_gmt":"2025-07-28T21:58:44","guid":{"rendered":"https:\/\/sarakhon.com\/?p=78200"},"modified":"2025-07-28T17:23:45","modified_gmt":"2025-07-28T11:23:45","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-245","status":"publish","type":"post","link":"https:\/\/sarakhon.com\/?p=78200","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\u09ef)"},"content":{"rendered":"<p><em>\u09b6\u09cd\u09b0\u09c7\u09a3\u09c0 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09c7 \u09ad\u09be\u09b0\u09a4\u09c0\u09df \u0997\u09a3\u09bf\u09a4\u09ac\u09bf\u09a6\u09c7\u09b0\u09be \u0986\u09b0\u0993 \u09ac\u09c7\u09b6\u09c0 \u099a\u09bf\u09a8\u09cd\u09a4\u09be-\u09ad\u09be\u09ac\u09a8\u09be \u0995\u09b0\u09be\u09b0 \u09ab\u09b2\u09c7 \u0986\u09b0\u0993 \u09a8\u09be\u09a8\u09be \u09a7\u09b0\u09a3\u09c7\u09b0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09c0\u09b0 \u09b8\u09be\u0995\u09cd\u09b7\u09be\u09ce \u09ae\u09bf\u09b2\u09a4\u09c7 \u09a5\u09be\u0995\u09c7\u0964<\/em><\/p>\n<p>\u09af\u09be\u09b0 \u09ae\u09ae\u09be\u09b0\u09cd\u09a5 \u09b9\u099a\u09cd\u099b\u09c7\u4e00<\/p>\n<p>a + (ar \u00b1 m) +{(ar \u00b1 m)\u00a0 r\u00b1 m } + [{(ar \u00b1 m)\u00a0 r + m} r \u00b1 m] +&#8230; +&#8230;&#8230;&#8230;.. +-\u09a4\u09ae \u09aa\u09a6\u0964<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-78201\" src=\"https:\/\/sarakhon.com\/wp-content\/uploads\/2025\/07\/7-54.jpg\" alt=\"\" width=\"221\" height=\"73\" \/><\/p>\n<p>s\u2018 = a + ar + a r\u00b3 +&#8230;&#8230;&#8230;&#8230;.. +n-\u09a4\u09ae \u09aa\u09a6\u0964<\/p>\n<p>\u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09df \u09ad\u09be\u09b8\u09cd\u0995\u09b0\u09be\u099a\u09be\u09b0\u09cd\u09af \u0997\u09c1\u09a3\u09cb\u09a4\u09cd\u09a4\u09b0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09c0 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09c7 \u0986\u09b2\u09cb\u099a\u09a8\u09be \u0995\u09b0\u09b2\u09c7\u0993 \u0995\u09bf\u099b\u09c1\u099f\u09be \u0985\u09b8\u09cd\u09aa\u09b7\u09cd\u099f \u098f\u09ac\u0982 \u09aa\u09cd\u09b0\u0995\u09c3\u09a4 \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u0985\u09a8\u09c1\u09aa\u09b8\u09cd\u09a5\u09bf\u09a4\u09bf \u09b2\u0995\u09cd\u09b7\u09cd\u09af \u0995\u09b0\u09be \u09af\u09be\u09df\u0964 \u09a4\u09ac\u09c7 \u09a4\u09bf\u09a8\u09bf \u0995\u09bf\u099b\u09c1 \u0989\u09a6\u09be\u09b9\u09b0\u09a3 \u09a6\u09bf\u09df\u09c7\u099b\u09c7\u09a8\u0964<br \/>\n\u09ac\u09be\u0995\u09cd\u0995\u09be\u09b2\u09c0\u09b0 \u09aa\u09be\u09a8\u09cd\u09a1\u09c1\u09b2\u09bf\u09aa\u09bf\u09a4\u09c7\u0993 \u09b6\u09cd\u09b0\u09c7\u09a3\u09c0\u09b0 \u09ac\u09cd\u09af\u09ac\u09b9\u09be\u09b0 \u09b2\u0995\u09cd\u09b7\u09cd\u09af \u0995\u09b0\u09be \u09af\u09be\u09df\u0964 \u09af\u09c7\u09ae\u09a8:<\/p>\n<p>\u09e7 (\u0995). a<sub>1 <\/sub>+ \u00a0+ 2a<sub>1 <\/sub> + 3a<sub>1 <\/sub> +&#8230;&#8230;&#8230;..+na<sub>1 <\/sub><\/p>\n<p>\u09e8(\u0996). a<sub>1<\/sub> + 2a<sub>1<\/sub> + 3a<sub>2<\/sub> +4a<sub>2<\/sub>&#8230;&#8230;+na <sub>n-1<\/sub><\/p>\n<p>\u09e9 (\u0997). a<sub>1<\/sub> + 2a<sub>1<\/sub> + 3( a<sub>1<\/sub> +a<sub>2\u00a0<\/sub>)+4 (a<sub>1<\/sub> + a<sub>2<\/sub>+a<sub>3<\/sub>)+&#8230;&#8230;..<\/p>\n<p>\u098f\u0987 \u09aa\u09cd\u09b0\u0995\u09cd\u09b0\u09bf\u09df\u09be\u0995\u09c7 \u09af\u09c1\u09a4\u09bf\u09ac\u09b0\u09cd\u0997\u0995\u09cd\u09b0\u09ae \u09ac\u09b2\u09be \u09b9\u09df\u09c7\u099b\u09c7\u0964 (\u0995), (\u0996) \u0993 (\u0997) \u098f\u09ac\u0982 \u099c\u09be\u09ae\u09be\u09a4<br \/>\nb+(b+d)+(b+2d)+\u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af \u09a8\u09bf\u09df\u09c7 \u09a8\u09bf\u09ae\u09cd\u09a8\u09cb\u0995\u09cd\u09a4 \u09b6\u09cd\u09b0\u09c7\u09a3\u09c0 \u0997\u09a0\u09bf\u09a4 \u09b9\u09df\u09c7\u099b\u09c7\u0964\u09e7<br \/>\ns().a\u2081+(2ab)+30+(b+d)+44+(b+2d)+<br \/>\n(5). a1+(24+b)-3a+(b+d)}+{4a,+(b+2d)}+<br \/>\n(5). a1+(241+b)+{3(a-a\u2082)(+b+d)}+{4(a,+a2+as) +(b+2d)<\/p>\n<p>\u098f\u0997\u09c1\u09b2\u09bf\u0995\u09c7 \u09b8\u09be\u09a7\u09be\u09b0\u09a3\u09a4 \u09af\u09c1\u09a4\u0997\u09a3\u09bf\u09a4 \u098b\u09a3\u0995\u09b0\u09cd\u09ae\u09c7\u09b0 \u09af\u09c1\u09a4\u0995\u09b0\u09cd\u09ae \u09ac\u09b2\u09be \u09b9\u09df\u09c7 \u09a5\u09be\u0995\u09c7\u0964 \u098f\u099b\u09be\u09dc\u09be\u0993 \u09ad\u09be\u09b0\u09a4\u09c0\u09df \u0985\u09a8\u09cd\u09af\u09be\u09a8\u09cd\u09af \u0997\u09a3\u09bf\u09a4\u0997\u09cd\u09b0\u09a8\u09cd\u09a5\u09c7 \u09b6\u09cd\u09b0\u09c7\u09a3\u09c0 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09c7 \u0986\u09b2\u09cb\u099a\u09a8\u09be \u0995\u09b0\u09be \u09b9\u09df\u09c7\u099b\u09c7\u0964 \u09af\u09be\u0987 \u09b9&#8217;\u0995 \u0986\u09ae\u09b0\u09be \u09b2\u0995\u09cd\u09b7\u09cd\u09af \u0995\u09b0\u09b2\u09be\u09ae \u09af\u09c7 \u09ac\u09c8\u09a6\u09bf\u0995 \u09b8\u09be\u09b9\u09bf\u09a4\u09cd\u09af\u09c7 \u09af\u09c1\u0997\u09cd\u09ae \u0993 \u0985\u09af\u09c1\u0997\u09cd\u09ae \u09b8\u0982\u0996\u09cd\u09af\u09be\u099c\u09be\u09a4 \u09b6\u09cd\u09b0\u09c7\u09a3\u09c0\u09b0 \u0989\u09b2\u09cd\u09b2\u09c7\u0996 \u09b0\u09df\u09c7\u099b\u09c7\u0964 \u09a4\u09be\u09b0\u09aa\u09b0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09c0 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09c7 \u09ad\u09be\u09b0\u09a4\u09c0\u09df \u0997\u09a3\u09bf\u09a4\u09ac\u09bf\u09a6\u09c7\u09b0\u09be \u0986\u09b0\u0993 \u09ac\u09c7\u09b6\u09c0 \u099a\u09bf\u09a8\u09cd\u09a4\u09be-\u09ad\u09be\u09ac\u09a8\u09be \u0995\u09b0\u09be\u09b0 \u09ab\u09b2\u09c7 \u0986\u09b0\u0993 \u09a8\u09be\u09a8\u09be \u09a7\u09b0\u09a3\u09c7\u09b0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09c0\u09b0 \u09b8\u09be\u0995\u09cd\u09b7\u09be\u09ce \u09ae\u09bf\u09b2\u09a4\u09c7 \u09a5\u09be\u0995\u09c7\u0964 \u098f \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09c7 \u09a8\u09ac\u09ae \u09b6\u09a4\u09be\u09ac\u09cd\u09a6\u09c0\u09a4\u09c7 \u09a8\u09c7\u09ae\u09c0\u099a\u09a8\u09cd\u09a6\u09cd\u09b0 \u09b2\u09bf\u0996\u09bf\u09a4 \u09a4\u09cd\u09b0\u09bf\u09b2\u09cb\u0995\u09b8\u09be\u09b0\u09c7 \u09e7\u09ea \u09a7\u09b0\u09a3\u09c7\u09b0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09c0\u09b0 \u0995\u09a5\u09be \u0989\u09b2\u09cd\u09b2\u09c7\u0996 \u0995\u09b0\u09be \u09b9\u09df\u09c7\u099b\u09c7\u0964<br \/>\n\u09af\u09a5\u09be:<\/p>\n<p>(\u09e7) \u09b8\u09b0\u09cd\u09ac \u0985\u09b0\u09cd\u09a5\u09be\u09ce 1, 2, 3 &#8230; # \u09b8\u09cd\u09ac\u09be\u09ad\u09be\u09ac\u09bf\u0995 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09a6\u09bf\u09b0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09c0<br \/>\n(\u09e8) \u09b8\u09ae \u0985\u09b0\u09cd\u09a5\u09be\u09ce 2,4,6 20 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09a6\u09bf\u09b0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09c0<br \/>\n(\u09e9) \u09ac\u09bf\u09b7\u09ae \u0985\u09b0\u09cd\u09a5\u09be\u09ce 1, 3, 5 (2pi &#8211; 1) \u09b8\u0982\u0996\u09cd\u09af\u09be\u09a6\u09bf\u09b0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09c0<br \/>\n(\u09ea) \u0995\u09c3\u09a4\u09bf \u0985\u09b0\u09cd\u09a5\u09be\u09ce 1\u00b2 28, 3\u00b2 n\u00b2 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09a6\u09bf\u09b0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09c0<br \/>\n(\u09eb) \u0985\u0995\u09c3\u09a4\u09bf, \u0985\u09ac\u09b0\u09cd\u0997 \u0985\u09b0\u09cd\u09a5\u09be\u09ce 2, 3, 5, 6 (-1) \u09b8\u0982\u0996\u09cd\u09af\u09be\u09a6\u09bf\u09b0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09c0<br \/>\n(\u09ec) \u0998\u09a8 \u0985\u09b0\u09cd\u09a5\u09be\u09ce 1\u00aa, 2\u00b3 3&#8243;, 48 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09a6\u09bf\u09b0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09c0 n\u00b3<br \/>\n(\u09ed) \u0985\u0998\u09a8 \u0985\u09b0\u09cd\u09a5\u09be\u09ce 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0998\u09a8\u09ae\u09c2\u09b2 \u0995\u09b0\u09be \u09af\u09be\u09df \u098f\u09ae\u09a8 \u09b8\u0982\u0996\u09cd\u09af\u09be \u09ac\u09be\u09a6 \u09a6\u09bf\u09df\u09c7 \u0985\u09a8\u09cd\u09af\u09be\u09a8\u09cd\u09af \u09b8\u0982\u0996\u09cd\u09af\u09be\u0964<br \/>\n(\u09ee) \u0995\u09c3\u09a4\u09bf\u09ae\u09be\u09a4\u09c3\u0995\u09be \u0985\u09b0\u09cd\u09a5\u09be\u09ce 1, 2 2. \u09b8\u0982\u0996\u09cd\u09af\u09be\u09a6\u09bf\u09b0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09c0 \u221an<br \/>\n(\u09e7) \u0985\u0995\u09c3\u09a4\u09bf\u09ae\u09be\u09a4\u09c3\u0995\u09be \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u221an+ 1 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09a6\u09bf\u09b0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09c0 \u221an + 2<br \/>\n(\u09e7\u09e6) \u0998\u09a8\u09ae\u09be\u09a4\u09c3\u0995<br \/>\n(\u09e7\u09e7) \u0985\u0998\u09a8\u09ae\u09be\u09a4\u09c3\u0995 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0985\u0998+1, \u0985\u0998+2, \u09b8\u0982\u0996\u09cd\u09af\u09be\u09a6\u09bf\u09b0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09c0<br \/>\n(\u09e7\u09e8) \u09a6\u09cd\u09ac\u09bf\u09b0\u09c2\u09aa\u09ac\u09b0\u09cd\u0997 \u0985\u09b0\u09cd\u09a5\u09be\u09ce 2 ^ z 2 ^ * 2 ^ n 2 ^ 16 2 ^ 32 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09a6\u09bf\u09b0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09c0<br \/>\n(\u09e7\u09e9) \u09a6\u09cd\u09ac\u09bf\u09b0\u09c2\u09aa\u0998\u09a8 \u0985\u09b0\u09cd\u09a5\u09be\u09ce 2 ^ 3 (2 ^ 3) ^ 9 (2 ^ 3) ^ 4 (2), (2) \u09b8\u0982\u0996\u09cd\u09af\u09be\u09a6\u09bf\u09b0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09c0<br \/>\n(\u09e7\u09ea) \u09a6\u09cd\u09ac\u09bf\u09b0\u09c2\u09aa\u0998\u09a8 \u0998\u09a8 \u0985\u09b0\u09cd\u09a5\u09be\u09ce (2 ^ 3) ^ 2 = 512 ((2 ^ 8) ^ 8) ^ 8 = 262144 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09a6\u09bf\u09b0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09c0<\/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\u09ee)<\/h4>\n<blockquote class=\"wp-embedded-content\" data-secret=\"gl8NiWD3Y8\"><p><a href=\"https:\/\/sarakhon.com\/?p=77859\">\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\u09ee)<\/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\u09ee)&#8221; &#8212; Sarakhon \u0964 \u09b8\u09be\u09b0\u09be\u0995\u09cd\u09b7\u09a3\" src=\"https:\/\/sarakhon.com\/?p=77859&#038;embed=true#?secret=JPoudGsJ46#?secret=gl8NiWD3Y8\" data-secret=\"gl8NiWD3Y8\" width=\"500\" height=\"282\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u09b6\u09cd\u09b0\u09c7\u09a3\u09c0 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09c7 \u09ad\u09be\u09b0\u09a4\u09c0\u09df \u0997\u09a3\u09bf\u09a4\u09ac\u09bf\u09a6\u09c7\u09b0\u09be \u0986\u09b0\u0993 \u09ac\u09c7\u09b6\u09c0 \u099a\u09bf\u09a8\u09cd\u09a4\u09be-\u09ad\u09be\u09ac\u09a8\u09be \u0995\u09b0\u09be\u09b0 \u09ab\u09b2\u09c7 \u0986\u09b0\u0993 \u09a8\u09be\u09a8\u09be \u09a7\u09b0\u09a3\u09c7\u09b0 \u09b6\u09cd\u09b0\u09c7\u09a3\u09c0\u09b0 \u09b8\u09be\u0995\u09cd\u09b7\u09be\u09ce \u09ae\u09bf\u09b2\u09a4\u09c7 \u09a5\u09be\u0995\u09c7\u0964 \u09af\u09be\u09b0 \u09ae\u09ae\u09be\u09b0\u09cd\u09a5 \u09b9\u099a\u09cd\u099b\u09c7\u4e00 a + (ar \u00b1 m) +{(ar \u00b1 m)\u00a0 r\u00b1 m } + [{(ar \u00b1 m)\u00a0 r + m} r \u00b1 m] +&#8230; +&#8230;&#8230;&#8230;.. +-\u09a4\u09ae \u09aa\u09a6\u0964 s\u2018 = a + ar + a r\u00b3 +&#8230;&#8230;&#8230;&#8230;.. +n-\u09a4\u09ae \u09aa\u09a6\u0964 [&hellip;]<\/p>\n","protected":false},"author":5,"featured_media":78202,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[38,17],"tags":[],"location":[],"class_list":["post-78200","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 \u09ae\u099c\u09c1\u09ae\u09a6\u09be\u09b0"},"audio_information":{"audio_link":"","audio_link_id":""},"seo_information":{"meta_keyword":""}},"_links":{"self":[{"href":"https:\/\/sarakhon.com\/index.php?rest_route=\/wp\/v2\/posts\/78200","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sarakhon.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sarakhon.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sarakhon.com\/index.php?rest_route=\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/sarakhon.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=78200"}],"version-history":[{"count":1,"href":"https:\/\/sarakhon.com\/index.php?rest_route=\/wp\/v2\/posts\/78200\/revisions"}],"predecessor-version":[{"id":78203,"href":"https:\/\/sarakhon.com\/index.php?rest_route=\/wp\/v2\/posts\/78200\/revisions\/78203"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sarakhon.com\/index.php?rest_route=\/wp\/v2\/media\/78202"}],"wp:attachment":[{"href":"https:\/\/sarakhon.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=78200"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sarakhon.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=78200"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sarakhon.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=78200"},{"taxonomy":"location","embeddable":true,"href":"https:\/\/sarakhon.com\/index.php?rest_route=%2Fwp%2Fv2%2Flocation&post=78200"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}