#1
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͹ءÃÁ¤ÃѺ
$\frac{1}{1^4+1^2+1}+\frac{2}{2^4+2^2+1}+....+\frac{100}{100^4+100^2+1}$
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#2
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$ \frac{1}{1^4+1^2+1}+\frac{2}{2^4+2^2+1}+....+\frac{100}{100^4+100^2+1} $ $ = \frac{1}{(1^2+1)^2-1^2}+\frac{2}{(2^2+1)^2-2^2}+....+\frac{100}{(100^2+1)^2-100^2} $ $ = \frac{1}{1\cdot3}+\frac{2}{3\cdot7}+....+\frac{100}{10101\cdot9901} $ $ = \frac{1}{2}\left( \frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{7}+...+\frac{1}{9901}-\frac{1}{10101}\right) $ $ = \frac{1}{2}\left( \frac{1}{1}-\frac{1}{10101}\right) $ $ = \frac{5050}{10101} $ |
#3
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¢Íº¤Ø³ÁÒ¡¤ÃѺ ä´é¤ÇÒÁÃÙéà¾ÔèÁÍÕ¡áÅéÊ
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