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#### sbhatnagar

##### Active member

- Jan 27, 2012

- 95

Hi everyone

I have a challenging problem which I would like to share with you.

Prove that

\[\frac{1}{2^2}+ \frac{1}{3^2} \left(1+\frac{1}{2} \right)^2+\frac{1}{4^2} \left( 1+\frac{1}{2} +\frac{1}{3}\right)^2 + \frac{1}{5^2} \left( 1+\frac{1}{2} +\frac{1}{3}+\frac{1}{4}\right)^2 +\cdots= \frac{11\pi^4}{360}\]

I have a challenging problem which I would like to share with you.

Prove that

\[\frac{1}{2^2}+ \frac{1}{3^2} \left(1+\frac{1}{2} \right)^2+\frac{1}{4^2} \left( 1+\frac{1}{2} +\frac{1}{3}\right)^2 + \frac{1}{5^2} \left( 1+\frac{1}{2} +\frac{1}{3}+\frac{1}{4}\right)^2 +\cdots= \frac{11\pi^4}{360}\]

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