# Thread: determine convergence or divergence of series

1. ## determine convergence or divergence of series

summation from n=1 to infinity ((n+1)0.5-(n)0.5)/(n2+n)​0.5.

I've tried using limit comparison test but the ratio i got approaches 0 and thus no conclusion can be drawn.

2. ## Re: determine convergence or divergence of series

note ...

$\dfrac{\sqrt{n+1} - \sqrt{n}}{\sqrt{n^2+n}} \cdot \dfrac{\sqrt{n+1} + \sqrt{n}}{\sqrt{n+1} + \sqrt{n}} = \dfrac{1}{\sqrt{n^2+n} (\sqrt{n+1} + \sqrt{n})} < \dfrac{1}{\sqrt{n^3}}$

what can you say about the series, $\displaystyle \sum \dfrac{1}{n^{3/2}}$ ... ?

3. ## Re: determine convergence or divergence of series

thats a p-series with power greater than 1 and hence converge. using comparison test, the series given also converge, Thanks for the help