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- Feb 14, 2012
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Let $x_1, x_2, x_3, x_4, x_5$ be real numbers satisfying the following equation:
$\dfrac{x_1}{m^2+1}+\dfrac{x_2}{m^2+2}+\dfrac{x_3}{m^2+3}+\dfrac{x_4}{m^2+4}+\dfrac{x_5}{m^2+5}= \dfrac{1}{m^2}$ for $m=1, 2, 3, 4, 5$.
Find the value of
$\dfrac{x_1}{37}+\dfrac{x_2}{38}+\dfrac{x_3}{39}+ \dfrac{x_4}{40}+\dfrac{x_5}{41}$
$\dfrac{x_1}{m^2+1}+\dfrac{x_2}{m^2+2}+\dfrac{x_3}{m^2+3}+\dfrac{x_4}{m^2+4}+\dfrac{x_5}{m^2+5}= \dfrac{1}{m^2}$ for $m=1, 2, 3, 4, 5$.
Find the value of
$\dfrac{x_1}{37}+\dfrac{x_2}{38}+\dfrac{x_3}{39}+ \dfrac{x_4}{40}+\dfrac{x_5}{41}$