For discussion:
this question is clearly a duplicate. However, I would argue that, as written, it is a contextless PSQ. The answer provides no information which is not already included in the dupe target. As such, there is not much point in keeping the question around.
I have to prove that:
$$\pi=\frac{27S-36}{8\sqrt{3}}$$
where I know that $$S=\sum_{n=0}^\infty\frac{\left(\left\lfloor\frac{n}{2}\right\rfloor!\right)^2}{n!}$$
Where do I get started?
Proof of $\sin nx=2^{n-1}\prod_{k=0}^{n-1} \sin\left( x + \frac{k\pi}{n} \right)$
Prove that $\prod_{k=1}^{n-1}\sin\frac{k \pi}{n} = \frac{n}{2^{n-1}}$
Prove that $\prod_{k=1}^{n-1}\sin\frac{k \pi}{n} = \frac{n}{2^{n-1}}$
Proof of $\sin nx=2^{n-1}\prod_{k=0}^{n-1} \sin\left( x + \frac{k\pi}{n}...
