Inverse Sum Cubed

Calculus Level 4

n=1(k=0nk3)1\large\displaystyle\sum_{n=1}^{\infty} \left({\displaystyle\sum_{k=0}^nk^3} \right)^{-1}

If the value of the series above can be expressed as aπ2bc\dfrac{a\pi^2}b-c where a,b,ca,b,c are positive integers, and a,ba,b are coprime to each other, find the value of a+b+ca+b+c.


See Also Inverse Sum and Inverse Sum Squared.

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