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Taylor Series Representation

  1. Apr 9, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the Taylor series of f(x) = x2ln(1+2x2) centered at c = 0.


    2. Relevant equations

    Taylor Series of f(x) = ln(1+x) is Ʃ from n=1 to ∞ of (-1)n-1xn/n

    3. The attempt at a solution

    I have worked the problem to

    (-1)n4nx2n/n

    I am not sure where to go from here

    Thank You!
     
  2. jcsd
  3. Apr 9, 2013 #2

    SammyS

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    Well, you seem to have the right idea for the Taylor series of ln(1+2x2). It's not quite right.

    [itex]\displaystyle \left(2x^2\right)^n=2^nx^{2n}\ .[/itex]

    When you make the correction for that, then just multiply by x2 , to get the Taylor series for x2ln(1+2x2).
     
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