# Math Help - Does the following series have a majorant series?

1. ## Does the following series have a majorant series?

A majorant series is a series that is equal or larger.
The series $\sum^{\infty}_{n=1}k_n$ is a majorant series to $\sum^{\infty}_{n=1}f_n(x)$ if:
$|f_n(x)|\leq k_n$

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?

2. ## Re: Does the following series have a majorant series?

How about $\sum_{n=0}^\infty 1$.

3. ## Re: Does the following series have a majorant series?

Originally Posted by HallsofIvy
How about $\sum_{n=0}^\infty 1$.
Yes, that is true.
my next question is whether or not a convergent majorant series exist? It doesn't seem like such a series exists?