↑は
http://www.math.ust.hk/excalibur/v14_n1.pdf
のp.3に出てた。orz
しかたないので一題･･･

Problem 2.
Let a_1 〜 a_5 be real numbers satisfying the following equations:
　a_1/(1+k^2) + a_2/(2+k^2) + a_3/(3+k^2) + a_4/(4+k^2) + a_5/(5+k^2),
for k=1〜5.　Find the value of
　a_1/37 + a_2/38 + a_3/39 + a_4/40 + a_5/41,
　(Express the value in a single fraction.)