# Inverse Sum Squared

Calculus Level 4

$\large\displaystyle\sum_{n=1}^{\infty}\left({\displaystyle\sum_{k=0}^nk^2}\right)^{-1}$ If the value of the series above can be expressed as $$a-b\ln{(c)}$$ where $$a,b$$ are positive integers and $$c$$ is the minimum possible positive integer, find the value of $$a+b+c$$.