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sum S=...+\frac{1}{1-x_{2004}^3}+...+\frac{1}{1-x_{2004}^{-3}}

Source: Greece JBMO TST 2004 p2

June 18, 2019

algebraSum

Problem Statement

Real numbers

x_1,x_2,...x_{2004},y_1,y_2,...y_{2004}

differ from

1

and are such that

x_ky_k=1

for every

k=1,2,...,2004

. Calculate the sum

S=\frac{1}{1-x_1^3}+\frac{1}{1-x_2^3}+...+\frac{1}{1-x_{2004}^3}+\frac{1}{1-y_1^3}+\frac{1}{1-y_2^3}+...+\frac{1}{1-y_{2004}^3}