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Math Help - Derivative of power series

  1. #1
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    Derivative of power series

    I have a function defined as a power series. I'm to show that f(0) = 0, and that f'(0) = 1.

    f(0) is obviously = 0, but when I take the derivative, what I get seems to also be equal to 0, not 1. Did I do the derivative wrong, or should this really equal 1?

    Thanks!
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  2. #2
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    Re: Derivative of power series

    Your derivative seems correct, I cannot see anything wrong with what you have written. 0 raised to the power of anything (except zero) equals zero and so the numerator will always be zero and the summation will just be a sum of zeros which will equal zero. Maybe you wrote down the question incorrectly?
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  3. #3
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    Re: Derivative of power series

    Nevermind I made a mistake

    EDIT: The derivative is actually \displaystyle{\sum_{n=0}^{\infty} \frac{(4n+1)z^{4n}}{(4n+1)!}}=1+\displaystyle{\sum  _{n=1}^{\infty} \frac{(4n+1)z^{4n}}{(4n+1)!}}
    Last edited by Gusbob; April 10th 2013 at 03:56 PM.
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