I'm not sure how to tag this question, as I don't know what area of math covers these problems.
For example, I know two or three ways of proving that $ S=\sum_{k=0}^{\infty}p^{k}=\frac{1}{1-p} $ if $|p|<1$. I'm sure others know more ways of showing this. What I'm interested in, if there exists some theorem or conjecture or area of mathematics that stipulates that there exists a finite/countable/uncountable number of ways of proving statements (even such simple as the one above).
If this question is too vague/inappropriate, I'd be happy to remove it from here.