# Does the following series have a majorant series?

• Dec 4th 2012, 08:49 AM
MathIsOhSoHard
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?
• Dec 4th 2012, 09:52 AM
HallsofIvy
Re: Does the following series have a majorant series?
How about $\displaystyle \sum_{n=0}^\infty 1$.
• Dec 4th 2012, 11:24 AM
MathIsOhSoHard
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?