3
$\begingroup$

Show that if $p>1$, $\sum\frac{1}{n^{p}}$ converges and if $p<1$ it diverges for $p\in\mathbb{R}^{+}$.

Is there any way to show another series converges or diverges and then use the Comparison Test to prove this?

  • 1
    This link [http://math.stackexchange.com/questions/29450/self-contained-proof-that-sum-limits-n-1-infty-frac1np-converges-for] could interest you.2012-01-21

4 Answers 4