#1
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͹ءÃÁ͹ѹµì
¨§ËҼźǡ¢Í§Í¹Ø¡ÃÁ͹ѹµì (¶éÒÁÕ)
$\frac{3}{1^2 \times 2^2}+ \frac{5}{2^2 \times 3^2}+\frac{7}{3^2 \times 4^2}+...+\frac{2n+1}{n^2 \times (n+1)^2}$ ¢Íº¤Ø³ÁÒ¡¤ÃѺ¼Á ÁÖ¹ÁÒ¡æ
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#2
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ÊѧࡵÇèÒ $(n+1)^2-n^2=2n+1$
´Ñ§¹Ñé¹ $\frac{2n+1}{n^2(n+1)^2}=\frac{(n+1)^2-n^2}{n^2(n+1)^2}=\frac{1}{n^2}-\frac{1}{(n+1)^2}$ à»ç¹Í¹Ø¡ÃÁ telescopic µÍº $1-\frac{1}{(n+1)^2}$ ¶éÒà»ç¹Í¹Ø¡ÃÁ͹ѹµì¡çµÍº $1$ ¤ÃѺ
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"ªÑèÇâÁ§Ë¹éÒµéͧ´Õ¡ÇèÒà´ÔÁ!" |
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