# Math Help - methods on determining convergence or divergence

1. ## methods on determining convergence or divergence

Can you use either taking the limit or solve the integral to find out if $\sum_{n=1}^\infty\frac{n}{\sqrt{n^2+1}}$ diverges or converges?

2. Originally Posted by Possible actuary
Can you use either taking the limit or solve the integral to find out if $\sum_{n=1}^\infty\frac{n}{\sqrt{n^2+1}}$ diverges or converges?
the limit test for divergence is the easiest method.

$\lim_{n \to \infty} \frac {n}{ \sqrt {n^2 + 1}} \neq 0$ thus the series diverges

3. Originally Posted by Possible actuary
Can you use either taking the limit or solve the integral to find out if $\sum_{n=1}^\infty\frac{n}{\sqrt{n^2+1}}$ diverges or converges?
The problem becomes harder if we consider $\sum_{n=1}^\infty\frac{n}{\sqrt{n^3+1}}$ or $\sum_{n=1}^\infty\frac{n}{\sqrt{n^4+1}}$