ζ(2)=π26!\displaystyle\zeta(2) =\frac{\pi^2}{6}!

Calculus Level 3

Given that

r=11r2=π26, \sum_{r=1}^{\infty} \frac{1}{r^2} = \frac{ \pi^2} { 6},

Evaluate the sum

r=01(2r+1)2. \displaystyle\sum_{r=0}^{\infty}\frac{1}{(2r+1)^2}.

Note: Do NOT use WolframAlpha.

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