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Write a partial sum for the power series,

  1. May 9, 2012 #1
    Write a partial sum for the power series, URGENT

    Consider the function ln(1+4x).
    Write a partial sum for the power series which represents this function consisting of the first 5 nonzero terms. For example, if the series were Sigma from n=0 to infinity of 3^nx^2n , you would write 1+3x2+3^2x^4+3^3x^6+3^4x^8. Also indicate the radius of convergence.

    I got a power series = Sigma from n=0 to infinity of [(-1)^n(4^2n+1)(x^n+1)] / n+1
    I got partial sum = 4x-32x^2+(1024/3)x^3-(16384/4)x^4+(262144/5)x^5
    and radius of convergence = 1/4

    radius of convergence is correct. But it says I have the partial sum wrong?
    please help!
     
  2. jcsd
  3. May 9, 2012 #2
    Re: Write a partial sum for the power series, URGENT

    This is wrong!

    Consider the simpler function:
    [tex]
    \ln(1 + y) = \sum_{n = 0}^{\infty}{\frac{(-1)^{n} y^{n + 1}}{n + 1}}
    [/tex]
    Then, take [itex]y = 4 x[/itex]. What does:
    [tex]
    (4 \, x)^{n + 1} = ?
    [/tex]
    equal to?
     
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