Is the series $\frac{1}{(n+1)^p}-\frac{1}{(n-1)^p}$ where 0Sorry for my bad English.
I really suspect it is convergent. But I can't prove it.
Since ${x^p}$ is not derivable at x=0, I can't using taylor expansion to find the order of infinitesimal, thus nth-term test cannot be used. I tried other test but they seem to  lead to a very complex expression.
Is the series convergent or divergen, and how to prove it ?
P.S. sorry for asking such a stupid question……

Notice that if 
$$a_n = \frac{1}{n^p} $$
The series you're asking about it equivalent to
$$ \sum_{n=2}^\infty a_{n+1} - a_{n-1} $$
Hint: It's telescoping.
