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Math Help - Series of Functions

  1. #1
    Newbie
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    Mar 2009
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    Series of Functions

    Hi,

    I would like to know how to prove the following:

    Prove that
    Summation of n from (0 to infinity): (e^-nx)(Sin nx)
    converges to a continuous function on (0,infinity)

    So, I will have to show it is uniform on [a,infinity) for every a > 0 and then what should I do next?

    Can someone please help me on this? Thank you!
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  2. #2
    MHF Contributor

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    Since it is clear that all of these functions are continuous for all n, showing that convergence is uniform is all you need!
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