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Homework Help: Power Series Help

  1. Apr 15, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the interval of convergence of f'(x)

    f(x) Sum from n=1 to infinity [(x-5)^n*(-1)^n]/[n5^n]



    2. Relevant equations



    3. The attempt at a solution

    My problem is I am unsure how to take the derivative with the n's and x's should I treat n as a constant?

    After that, I think I can get the interval of convergence.
     
  2. jcsd
  3. Apr 15, 2008 #2
    Is the derivative the sum from n=1 to infinity of [(x-5)^(n-1) * (-1)^(n+1)]/[5^n]?????
     
    Last edited: Apr 15, 2008
  4. Apr 15, 2008 #3

    Dick

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    Almost. How did (-1)^n become (-1)^(n+1)?
     
  5. Apr 15, 2008 #4
    Oh... it should be (-1)^(n+1) in the original function, I just typed it out wrong.
     
  6. Apr 15, 2008 #5

    Dick

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    It looks fine then.
     
  7. Apr 15, 2008 #6
    yes you just treat n as a constant.

    Be careful when taking the derivative of a series though. Here the issue didn't come up, but if you have x^n where n starts at 0 and end up with x^(n-1) where n starts at 0 then you would get x^(-1) for n=0 which is a no-no so you'd have to move you n up to starting at 1 do solve that problem.
     
  8. Apr 15, 2008 #7
    I think finding R for the original function should be enough; differentiation does not change R.

    Using this way, you get R = 5?
     
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