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.
2026-04-06 22:16:59.1775513819
Closed form for $\sum_{k=1}^{\infty} \zeta(2k)-\zeta(2k+1)$
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Writing zeta-functions as series and changing the summation order does the trick.