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Power Series

  1. Mar 26, 2008 #1
    1. The problem statement, all variables and given/known data
    Prove that the following sums only converge at 0.
    sum of: e^(n^2)*x^n , and
    sum of: e*n^(n)*x^(n)


    2. Relevant equations
    well i know series converge if the lim as n approaches inf of the abs(x-c) is less than (An/An+1) but I have no idea how to prove it, I saw these for the first time yesterday in class, and dont know much about it.


    3. The attempt at a solution
     
  2. jcsd
  3. Mar 26, 2008 #2

    HallsofIvy

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    Whart you are talking about is the "ratio test" for power series. What is An+1/An for these series?
     
  4. Mar 26, 2008 #3

    dynamicsolo

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    Are you missing either division signs or negative signs in exponents somewhere? I don't see how these are going to converge to zero as you've written them...
     
  5. Mar 27, 2008 #4

    HallsofIvy

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    He didn't say they converge to 0, he said they only converge at x= 0.
     
  6. Mar 27, 2008 #5

    dynamicsolo

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    Sorry, missed the 'only'; I've read too many sentences with wrong prepositions lately and thought the OP meant 'to'. (Your mentioning the Ratio Test reinforced this...)

    The first question might be: how do you write the power series for these exponential functions? What do you get when you multiply them by x^n?
     
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