# Logs as an infinite sum

Calculus Level 4

$\large \sum_{n=2}^\infty \dfrac{(-1)^n}{n-n^2}$

If the series above is in the form of $$A - B\ln C$$, where $$A,B,C$$ are positive integers with $$C$$ square-free, find $$A+B+C$$.

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