I am interested in the following sum for a given value of n:
$ \sum\limits_{x=1}^{n} \sum\limits_{y=1}^{n}x^y$
I can simplify this to
$ \sum\limits_{x=1}^{n} \frac{x^{n+1} - x}{x - 1}$
From here I can't see any way to further simplify this. Is there an exact value for this sum? If not, is there an algorithm to calculate it efficiently?