methods on determining convergence or divergence

**Possible actuary** · July 9th 2007, 03:52 PM

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?

**Jhevon** · July 9th 2007, 04:13 PM

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

**curvature** · July 9th 2007, 06:23 PM

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 $\sum_{n=1}^\infty\frac{n}{\sqrt{n^4+1}}$

Thread: methods on determining convergence or divergence