1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Uniform convergence of series

  1. Aug 31, 2010 #1
    1. The problem statement, all variables and given/known data

    Does the following series converge uniformly?

    [sum from n=1 to inf] [itex]\frac{e^{-nx}}{n^2} [/itex] 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?

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

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Aug 31, 2010 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook