Does This Series Converge Uniformly on [0, ∞)?

[Namo]

Homework Statement

Does the following series converge uniformly?

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

Homework 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.

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

 

[Office_Shredder]

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