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ÁÕ⨷ÂìÁÒãËéÅͧ·Ó
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⨷Âì·Õè¶ÒÁÁÒä´é¤èÒÅÔÁÔµà»ç¹ $\infty$ ¤ÃѺ áµè
$$\lim_{n\to\infty}\frac{1^k+2^k+\cdots+n^k}{n^{k+1}}=\lim_{n\to\infty}\frac{1}{n}\Big[\Big(\frac{1}{n}\Big)^k+\cdots +\Big(\frac{n}{n}\Big)^k\Big]=\int_0^1x^k\, dx = \frac{1}{k+1}$$
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site:mathcenter.net ¤Ó¤é¹ 15 ¾ÄÉÀÒ¤Á 2007 14:03 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 2 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ nooonuii |
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ªèÇ»ÅØ¡¡ÃзÙé
¨§ËÒ¤èҢͧ\[ \mathop {\lim }\limits_{x \to \frac{\pi }{2}} \frac{{\ln \left[ {\sin \left( {4m + 1} \right)x} \right]}}{{\ln \left[ {\sin \left( {4n + 1} \right)x} \right]}} \] àÁ×èÍ \[ \left\{ {m,n} \right\} \subset z \] |
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