Does the following series have a majorant series?

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?

http://i969.photobucket.com/albums/a...1/equation.gif

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?

Re: Does the following series have a majorant series?

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

Re: Does the following series have a majorant series?

Quote:

Originally Posted by

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

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?