# Uniform convergence of series

1. Aug 31, 2010

### Namo

1. The problem statement, all variables and given/known data

Does the following series converge uniformly?

[sum from n=1 to inf] $\frac{e^{-nx}}{n^2}$ on [0, inf)

2. Relevant equations

I know I need to use the M test or Cauchys Principle of uniform convergence. My tutor suggests using the former if there is uniform convergence & the latter if there isn't.

3. The attempt at a solution

I tried converting the exponential into summation form to see if that would help, but it didn't get me anywhere. I can't really see any easy way to use the M test.

Could anyone point me in the right direction as to start this problem?

Cheers
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Aug 31, 2010

### Office_Shredder

Staff Emeritus
nx is positive, so what's the first thing that comes to mind to bound e-nx?

You almost never want to turn an exponential into its power series form to answer a question like this