- #1

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[tex]

\frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + ... = \frac{\pi^2}{6}

[/tex]

There are various well-known ways to prove this.

I was wondering if there is a similar, simple way to calculate the value of the sum:

[tex]

\frac{1}{1^2} - \frac{1}{2^2} + \frac{1}{3^2} - \frac{1}{4^2} + ... = ???

[/tex]

The value of this sum should work out to pi*pi/12, but I was wondering if there was a straightforward way to prove it?