It is an elementary mathematical analysis problem, but I have some problem solving that.
Show that the sequence $1/n^k$ ,where $n \in \mathbb{N}$ is a natural number, is convergent if and only if $ k \geq 0$, and that the limit is $0$ for all $k > 0$.
I really don't know how to prove that when $ 0\leq k < 1$, the sequence is convergent.