Function sequence $(f_n)$ is defined as $f_n(x) :=\frac{1}{n^2} \sum_{i=1}^n i^x$ for $x \in \mathbb{R}$.
- I was wondering how to decide its convergence region? If it were a p-series, then there was some standard result, but it isn't a p-series.
- In particular, what is the region where $(f_n)$ converges to $0$?
Thank you!