# Logs as an infinite sum

**Calculus**Level pending

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

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 \(A+B+C\).

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

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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