From WolframAlpha it seems that $$ \frac{1}{2}=\sum_{k=1}^{\infty} \zeta(2k)-\zeta(2k+1) $$
Could someone provide a proof for this?
Thanks.
From WolframAlpha it seems that $$ \frac{1}{2}=\sum_{k=1}^{\infty} \zeta(2k)-\zeta(2k+1) $$
Could someone provide a proof for this?
Thanks.
Writing zeta-functions as series and changing the summation order does the trick.