Infinite Series

**saiyanmx89** · March 28th 2009, 01:51 PM

Determine convergence or divergence:

$a_n = \frac {1+(-1)^n}{n^2}$

Does the this function converge and is the limit equal to 0? That is what I found it to be.

**Jhevon** · March 28th 2009, 02:11 PM

Originally Posted by saiyanmx89

Determine convergence or divergence:

$a_n = \frac {1+(-1)^n}{n^2}$

Does the this function converge and is the limit equal to 0? That is what I found it to be.

yes. one way to see this is to use the squeeze theorem

**Twig** · March 28th 2009, 03:16 PM

hi

I guess you could do

$\frac{1 +(-1)^{n}}{n^{2}} \, \leq \, \frac{(-1)^{n}}{n^{2}}$

And the series to the right is converging by Leibniz convergence theorem, because the series is alternating and decreasing.