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#1
30 ÁÕ¹Ò¤Á 2001, 17:41
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͹ءÃÁ
ËÒ¤èҨӹǹ¨ÃÔ§ x ·Õè·ÓãËé
sigma (n=1 to infinity ) [ 1/n - sin(1/n)] converge 
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#2
30 ÁÕ¹Ò¤Á 2001, 17:41
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â·É·Õ¤ÃѺ Å×Á¾ÔÁ¾ì ·Õè¶Ù¡¤×Í
[ 1/n - sin(1/n) ]^x
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#3
30 ÁÕ¹Ò¤Á 2001, 17:42
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à´ÕëÂÇÅͧ¤Ô´´Ù¡è͹¤ÃѺ
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#4
30 ÁÕ¹Ò¤Á 2001, 17:42
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¨Ò¡¤ÇÒÁÃÙé¢Í§Í¹Ø¡ÃÁà·àÅÍÃì
sin x = x/1! - x^3/3! + x^5/5! - x^7/7!... ¨Ðä´éÇèÒ sin (1/n) = (1/n)/1! -(1/n^3)/3! + (1/n^5)/5! ... ´Ñ§¹Ñé¹ [1/n -sin (1/n) ]^x = [ 1/n^3)/3! - (1/n^5)/5! + (1/n^7)/7!...]^x «Öè§àÁ×èÍÅͧ¡ÃШÒ¾¨¹ì´Ù¤ÃèÒÇæ¨Ð¾ºÇèÒ·Ø¡¾¨¹ìà¢Õ¹ä´éã¹ÃÙ»¢Í§ c*(1/n^k) ; c,k = ¨Ó¹Ç¹¨ÃÔ§ «Öè§àÁ×èÍàÍÒ sigma ¡ÃШÒÂà¢éÒä»ã¹·Ø¡æ à·ÍÁ ¨Ð¾ºÇèÒ áµèÅÐà·ÍÁ¹Ñé¹à»ç¹Í¹Ø¡ÃÁ p (p-series) ͹ءÃÁ p --> sigma (n=1 to infinity) 1/n^p ¨Ð converge àÁ×èÍ p > 1 (p = ¨Ó¹Ç¹¨ÃÔ§) ¹Ñ蹤×Í Í¹Ø¡ÃÁ¹Õé¨Ð converge àÁ×èÍ Í¹Ø¡ÃÁ p ã¹·Ø¡à·ÍÁ converge «Öè§àÁ×è;ԨÒóҾ¨¹ì·ÕèÁÕ degree µèÓÊØ´¤×Í ¾¨¹ì sigma( ) (1/n^(3*x)] ¾¨¹ì¹Õé¨Ð converge àÁ×èÍ 3*x >1 ä´éÇèÒ x > 1/3 Êèǹ¾¨¹ìÍ×è¹æ ·ÕèÁÕ degree ÊÙ§¡ÇèÒ¹Õé ÊÒÁÒöÅСÒþԨÒóÒä´éà¹×èͧ¨Ò¡ àÁ×èÍ x> 1/3 áÅéÇ Í¹Ø¡ÃÁ p ã¹¾¨¹ìÍ×è¹æ ·Ø¡æà·ÍÁ¨Ð converge ä»´éÇ ´Ñ§¹Ñé¹Í¹Ø¡ÃÁ¹Õé converge àÁ×èÍ x>1/3
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