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Math Help - Power Series Differentiation & Integration

  1. #1
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    Power Series Differentiation & Integration

    Hi,

    the question asks for the derivative of

    Sigma notation (n=0) [(2nx^n) / (2n+1)]

    Is it just f'(x) = 2(n^2)(x^(n-1))?

    The second part asks for the integral of the above power series so that F(0) = 0?
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  2. #2
    MHF Contributor kalagota's Avatar
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    Taguig City, Philippines
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    Quote Originally Posted by shogunhd View Post
    Hi,

    the question asks for the derivative of

    Sigma notation (n=0) [(2nx^n) / (2n+1)]

    Is it just f'(x) = 2(n^2)(x^(n-1))?

    The second part asks for the integral of the above power series so that F(0) = 0?
    yes, but don't forget the denominator..

    note: A power series can be differentiated/integrated term by term over any closed and bounded interval inside the radius of convergence..
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