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Finite Sum of Power?
Suppose $f(s,k) = \sum_{n=1}^k n^{-s}$ is the Riemann zeta function truncated at the k-th term. I read on mathoverflow that there is a formula for $f(s,k)$ in terms of Bernoulli numbers, but I can't find it on the web. Would someone happen to know it or could point to a link? I am primarily interested in the case when $s$ is a negative real number.
Thanks!