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Prove that the real part of this limit converges to $\frac{1}{2}$
Let $s= 1/3 + 14i$.
Prove that the real part of this limit converges to $\frac{1}{2}$:
$$
\Re\lim_{n \rightarrow \infty}
\left(
\left[
1-
\left(
\sum _{k=1}^n \frac{(-1)^{k-1} \binom{n-1}{...
- 1,183
0
votes
1
answer
138
views
proving inequality in Riemann zeta function
Recently I have made some interesting observations on the limit $$\lim_{k\rightarrow \infty}{\sum_{n=1}^{k}{\dfrac{(-1)^{n-1}\biggl( \cos \left(\beta\ln(n)\right)\biggr)}{n^{\alpha}}}}. $$ When this ...
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