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Tagged with examples riemann-zeta-function
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Elementary functions such that $\sum_{n=2}^{\infty} f(n) \left( \zeta(n)-1 \right)$ can be evaluated, but $\sum_{n=2}^{\infty} f(n)$ can't
Background
The general context for this question is the topic of rational zeta series. What I've found so far, is that it usually the case that sums of the form $$\zeta_{f} := \sum_{n=2}^{\infty} f(n) ...
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Example of an integer $n_0$ such that $1+\sum_{k=2}^{n_0} \zeta(k)^s=0$ has repeated roots
After I was studying the exercise Problem 4.20 from [1] I was inspired to ask about next problem, where $\zeta(k)$ denotes, for integers $k>1$, particular values of the Riemann zeta function. And $...
