Test ͹ءÃÁ¤ÃѺ
1) $\sum_{n = 2}^{\infty} \frac{1}{n ln n} $
2) $\sum_{n = 1}^{\infty} \frac{n ln n}{(n+1)^4} $ ¤Ô´ÍÍ¡áµè integral test ÁÕÇÔ¸Õ§èÒ¡ÇèÒ¹ÕéÁÑé¤ÃѺ |
2. àÅ×Í¡ $b_n=\frac{n}{(n+1)^{2.5}}$
¨Ðä´é sum bn ÅÙèà¢éÒ ËÒÅÔÁÔµ an/bn ¨Ðä´é0 ´Ñ§¹Ñé¹ sum an ÅÙèà¢éÒ ¢ÍÍÀÑÂäÁèÊдǡ¾ÔÁ¾ì latex |
ÍéÒ§ÍÔ§:
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2. $\dfrac{n\ln n}{(n+1)^4}\leq \dfrac{1}{n^2}$
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¢éÍ 1 ÅͧÃÇÁ¾¨¹ì¤ÃÑé§ÅÐ $2^n$ ¾¨¹ì´Ù¤ÃѺ
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ÍéÒ§ÍÔ§:
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¼Á·ÓÍÂèÒ§¹Õé¤ÃѺ $$\sum_{r=2^n+1}^{2^{n+1}}\frac{1}{r\log r}\geq \frac{2^n}{2^{n+1}\log 2^{n+1}}=\frac{1}{2(\log 2)(n+1)}$$
´Ñ§¹Ñé¹ $$\sum_{n=2}^{\infty}\frac{1}{n\log n}=\sum_{n=1}^{\infty}\sum_{r=2^n+1}^{2^{n+1}}\frac{1}{r\log r}\geq\sum_{n=1}^{\infty}\frac{1}{2(\log 2)(n+1)}$$ «Öè§àËç¹ä´éªÑ´ÇèÒÅÙèÍÍ¡¤ÃѺ |
ÍÖÁ ÇÔ¸Õ¤Ô´àËÁ×͹¾Ç¡µÓÃÒâÍÅÔÁ»Ô¤ÇÔªÒ¡Òà àŤÃѺ à¨ÍÃÙ»ÊÁ¡Òà äÁèÁÕÀÒ¾¨Ð§§ ÎèÒæ
¹Ñº¡ÒÃà¢éÒ¤Ù褹à»ç¹Ç§¡ÅÁ ËÃ×Í áºè§à«¡ªÑ蹢ͧǧ¡ÅÁ ¤ÃѺ |
àÇÅÒ·ÕèáÊ´§·Ñé§ËÁ´ à»ç¹àÇÅÒ·Õè»ÃÐà·Èä·Â (GMT +7) ¢³Ð¹Õéà»ç¹àÇÅÒ 11:18 |
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