Difference between revisions of "AoPS Wiki talk:Problem of the Day/August 3, 2011"

Solution

Since $\sum_{n=1}^{\infty}\dfrac{5^n+n}{n} = \sum_{n=1}^{\infty}\left(1+\frac{5^n}{n}\right)$, the sum diverges, since the sum is always greater than the index, due to constant 1.