For example, in this problem (trying to determine convergence):
$$\sum\limits_{n=1}^\infty \frac{\cos\left(\dfrac{1}{n}\right)}{n^2}$$
Can I just compare this ($a_n$):
$$\frac{\cos\left(\dfrac{1}{n}\right)}{n^2}$$
to this? ($b_n$):
$$\cos\left(\dfrac{1}{n}\right)$$
$\cos(1/n)$ converges at 1 and $a_n \le b_n$ so the original summation converges, yes? I was just wondering the rules for choosing $b_n$. Can I just choose something completely arbitrary and not at all related to the original equation?