Let $s_n(a)=1^a+2^a+\cdots+n^a$ where $a$ is real. Determine:
I can show that it converges. I can also find the limit for particular case when $a=0$. I think I could find a formula for natural numbers and prove it by induction. But since $a$ is real, I am stuck. Any tips of how should I proceed? Thanks!