# Multiple Partial Fractions

Algebra Level 4

Given that $$k\in\mathbb{Z}^+$$ is a constant and the expression of $\frac{x^3+x^2+x+k}{(x+k)^2 (x^2+k^2)}$

into partial fractions is $\frac{C_{k,1}}{(x+k)}+\frac{C_{k,2}}{(x+k)^2}+\frac{(C_{k,3})(x)+C_{k,4}}{(x^2+k^2)}$

where $$C_{k,1}, C_{k,2}, C_{k,3}, C_{k,4}$$ are constants, determine the value of $\sum_{k=2}^{50} {C_{k,2}}-25$

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