How do you test the series Sigma 1/sqrt(n(n+1)) from n is [1,oo) for convergence?

Jan 27, 2017

See below.

Explanation:

$\frac{1}{n + 1} < \frac{1}{\sqrt{n \left(n + 1\right)}} < \frac{1}{n}$

and

$\sum \frac{1}{n}$ does not converge

so

$\sum \frac{1}{\sqrt{n \left(n + 1\right)}}$ does not converge!