I am trying to determine the limit of the following expression which arose when looking at correlations for a stochastic process.

$\lim\_{n \to +\infty} ((n+1)^a-n^a)$ for values of $a\in (0,2)$.

I'm not sure how to approach this. I am aware that for $a>1$ the limit equals $\infty$ and for $a<1$ the limit is $-1$ (and $a=0 \implies$ limit $=0$).

Any ideas of what to try here would be greatly appreciated.