The first time I saw this serie is in an article titled “Examples of series approximating $\pi$”. It was said that the most beautiful formula among a lot is this:
$$\pi=\frac{9801}{2\sqrt{2}\sum_{n=0}^{+\infty}\frac{(4n)!}{(n!)^{4}}\frac{1103+26390n}{396^{4n}}}$$ by Ramanujan.
My question is what makes this formula so beautiful?
"Beauty" could mean the fact that there is no reason why the combination of numbers put forth should ever be seen to have anything to do with $\pi$ by mere mortals. Or the fact that the series converges so damn quickly.