# Thread: Another limit comparison series

1. ## Another limit comparison series

I suck at these. Anyway, can someone tell me how to start this one please?

$\displaystyle \sum^{\infty}_{n=1} \frac{cos^2(n)}{n^4 + 1}$

2. $\displaystyle \frac{\cos ^{2}n}{n^{4}+1}<\frac{1}{n^{4}}.$

3. Recall that: $\displaystyle 0 \leq \cos^2 x \leq 1$

So: $\displaystyle \frac{\cos^2 n}{n^4 + 1} \leq \frac{1}{n^4 + 1} < \frac{1}{n^4}$

4. Note that $\displaystyle 0<cos^2(n)<1$. THUS....

Originally Posted by mollymcf2009
I suck at these. Anyway, can someone tell me how to start this one please?

$\displaystyle \sum^{\infty}_{n=1} \frac{cos^2(n)}{n^4 + 1} <\sum^{\infty}_{n=1} \frac{1}{n^4}<\infty$
via p=4