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Results tagged with elementary-proofs
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user 9025
For questions related to 'elementary' proofs in a technical sense, which has nothing to do with the difficulty of the argument or result. A typical example would be 'elementary' proofs of the Prime Number Theorem, which avoid complex analysis. The tag is however not limited to this particular notion of 'elementary.'
25
votes
Accepted
A conjectural infinite series for $\frac{\pi^2}{5\sqrt{5}}$
More generally, if $1\le k\le N-1$ is an integer, where $N$ is a positive interger,
$$S_{N,k} := \sum_{n=0}^\infty\biggl( \frac{1}{(N n+N-k)^2} + \frac{1}{(N n+k)^2}
\biggr) = \frac{\pi^2}{N^2\sin^ …
- 37.7k