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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?

    Cheers
    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

    Office_Shredder

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    Staff Emeritus
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    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
     
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