I’m trying to get a closed form for
$$\sum_{n=k}^\infty n^{-\beta}\;,$$
where $\beta>\frac12$ and $k>0$.
Any help is appreciated. Thanks.
2026-03-29 18:00:43.1774807243
Closed form for an infinite series wanted.
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You could subtract the formula for the sum of the first $k$ numbers to the $nth$ power from the Riemann Zeta function. As pointed out in the comments, this is only valid when it converges.