# Summation of an Infinite Series

• January 13th 2013, 11:17 PM
sbhatnagar
Summation of an Infinite Series
Show that

$\sum_{n=1}^\infty \frac{\zeta(2n)}{n 2^{2n}} = \ln \left( \frac{\pi}{2}\right)$
• January 20th 2013, 07:09 PM
zaidalyafey
Re: Summation of an Infinite Series
I used the equality : $\Gamma(s) \zeta(s) = \int^{\infty}_0 \frac{t^{s-1}}{e^t-1}\,dt$

and got $\,2\int^{\infty}_0 \frac{\cosh(\frac{t}{2})-1}{t(e^t-1)}\, dt$

I am still trying to find this integral , (Headbang)