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µÍº 1/2 ¤ÃѺ ÇÔ¸Õ¼ÁäÁè·ÃÒº
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à¹×èͧ¨Ò¡ ͹ءÃÁ·Ñé§ÊͧÅÙèà¢éҹФÃѺ ¡ç¨Ðä´éÇèÒ
\[ 1-\frac{1}{2^2} + \frac{1}{3^2} - \frac{1}{4^2} +... =(1+\frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} +...) - 2(\frac{1}{2^2} + \frac{1}{4^2} + \frac{1}{6^2} +...) = \frac{1}{2}(1+\frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} +...) \] ¡çÊÒÁÒöÊÃØ»ä´éÇèÒ \[\frac{1-\frac{1}{2^2} + \frac{1}{3^2} - \frac{1}{4^2} +...}{1+\frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} +...} = \frac{1}{2} \] ¤ÇÒÁ¹èÒʹ㨢ͧ͹ءÃÁ¹Õé¤×Í \[ 1+\frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} +... = \frac{\pi^2}{6} \]
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¨§ËÒ¤èҢͧ a1 + a2 + a3 + a4 + a5 + ... + a24 àÁ×èÍ¡Ó˹´ãËé
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µéͧËÑ´ãªé Latex ºéÒ§áÅéÇ à´ÕëÂÇÅ×ÁËÁ´
$\frac{1}{\sqrt{n+\sqrt{n^2-1}}} \cdot \frac{\sqrt{n-\sqrt{n^2-1}}}{\sqrt{n-\sqrt{n^2-1}}}$ $= \sqrt{n - \sqrt{n^2-1}} = \sqrt{\frac{2n-2\sqrt{n^2-1}}{2}}$ $= \frac{\sqrt{(n+1) + (n - 1) - 2\sqrt{(n+1)(n-1)}}}{\sqrt{2}}$ $= \frac{1}{\sqrt{2}} \cdot (\sqrt{n+1} - \sqrt{n-1})$ àÁ×èÍá·¹¤èÒ¡ç¨ÐµÑ´¡Ñ¹ä´éã¹·ÕèÊØ´ |
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$ 2\sqrt{3} + 2\sqrt{2} $ ¶Ö§¨Ðà¡èÒáµè¼ÁàËç¹ÇèÒÁѹ¹èÒ·Ó´Õ ¡çàÅ¢͵ͺ¹Ð¤ÃѺ 07 àÁÉÒ¹ 2009 21:08 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ Aphenisol |
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