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Four infinite series involving Riemann zeta function
Can you provide a proof for at least one of the claims given below?
It is known that $\pi=\displaystyle\sum_{n=1}^{\infty}\frac{3^n-1}{4^n} \cdot \zeta(n+1)$ where $\zeta$ denotes Riemann zeta ...
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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 $...
