Inverse Sum Squared

Calculus Level 5

n=1(k=0nk2)1\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 abln(c)a-b\ln{(c)} where a,ba,b are positive integers and cc is the minimum possible positive integer, find the value of a+b+ca+b+c.


See Also Inverse Sum and Inverse Sum Cubed.

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