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ÊÁѤÃÊÁÒªÔ¡ ¤ÙèÁ×Í¡ÒÃãªé ÃÒª×èÍÊÁÒªÔ¡ »¯Ô·Ô¹ ¤é¹ËÒ ¢éͤÇÒÁÇѹ¹Õé ·Óà¤Ã×èͧËÁÒÂÍèÒ¹·Ø¡ËéͧáÅéÇ

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Old 28 ¡ØÁÀҾѹ¸ì 2016, 00:04
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1) $\sum_{n = 2}^{\infty} \frac{1}{n ln n} $
2) $\sum_{n = 1}^{\infty} \frac{n ln n}{(n+1)^4} $
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28 ¡ØÁÀҾѹ¸ì 2016 02:32 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 3 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ ¤usÑ¡¤³Ôm
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  #2  
Old 28 ¡ØÁÀҾѹ¸ì 2016, 17:19
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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

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28 ¡ØÁÀҾѹ¸ì 2016 19:33 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 2 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ polsk133
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  #3  
Old 28 ¡ØÁÀҾѹ¸ì 2016, 18:31
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ÍéÒ§ÍÔ§:
¢éͤÇÒÁà´ÔÁà¢Õ¹â´Â¤Ø³ polsk133 View Post
2. àÅ×Í¡ $b_n=\frac{n}{(n+1)^{2.5}}$
¨Ðä´é bn ÅÙèà¢éÒ ËÒÅÔÁÔµ an/bn ¨Ðä´é0 ´Ñ§¹Ñé¹ an ÅÙèà¢éÒ

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  #4  
Old 28 ¡ØÁÀҾѹ¸ì 2016, 21:24
nooonuii nooonuii äÁèÍÂÙèã¹Ãкº
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2. $\dfrac{n\ln n}{(n+1)^4}\leq \dfrac{1}{n^2}$
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  #5  
Old 02 ÁÕ¹Ò¤Á 2016, 16:52
Pitchayut Pitchayut äÁèÍÂÙèã¹Ãкº
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¢éÍ 1 ÅͧÃÇÁ¾¨¹ì¤ÃÑé§ÅÐ $2^n$ ¾¨¹ì´Ù¤ÃѺ
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  #6  
Old 02 ÁÕ¹Ò¤Á 2016, 20:10
nooonuii nooonuii äÁèÍÂÙèã¹Ãкº
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ÍéÒ§ÍÔ§:
¢éͤÇÒÁà´ÔÁà¢Õ¹â´Â¤Ø³ Pitchayut View Post
¢éÍ 1 ÅͧÃÇÁ¾¨¹ì¤ÃÑé§ÅÐ $2^n$ ¾¨¹ì´Ù¤ÃѺ
ÃÇÁÂѧä§àËÃͤÃѺ ÍÂÒ¡ÃÙéÁÒ¡à¾ÃÒеÑǹÕé¶éÒäÁèãªé integral test ¨ÐÂÒ¡ÁÒ¡
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  #7  
Old 03 ÁÕ¹Ò¤Á 2016, 16:09
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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 $$\sum_{n=2}^{\infty}\frac{1}{n\log n}=\sum_{n=1}^{\infty}\sum_{r=2^n+1}^{2^{n+1}}\frac{1}{r\log r}\geq\sum_{n=1}^{\infty}\frac{1}{2(\log 2)(n+1)}$$
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  #8  
Old 08 ¸Ñ¹ÇÒ¤Á 2016, 21:35
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