A majorant series is a series that is equal or larger.

The series $\displaystyle \sum^{\infty}_{n=1}k_n$ is a majorant series to$\displaystyle \sum^{\infty}_{n=1}f_n(x)$ if:

$\displaystyle |f_n(x)|\leq k_n$

Does the following series have a majorant series?

I'm not sure what arguments to use here. Cosine's maximum value can only be 1 but how do I find a series that can be equal to or larger than this?