Results 1 to 2 of 2

Math Help - power series

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    21

    power series

    find a power series representation

    f(x)=(x^2) \ (1-2x)^2

    how do i do this??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by mathlovet View Post
    find a power series representation

    f(x)=(x^2) \ (1-2x)^2

    how do i do this??
    Remember that, \sum_{n=0}^{\infty} x^n = \frac{1}{1-x} for |x| < 1.

    Thus, \left( \sum_{n=0}^{\infty} x^n \right)' = \left( \frac{1}{1-x} \right)' \implies \sum_{n=1}^{\infty}nx^{n-1} = \frac{1}{(1-x)^2} for |x| < 1

    This gives us,
    \sum_{n=1}^{\infty} nx^{n+1} = \frac{x^2}{(1-x)^2}, |x|<1

    Thus,
    \sum_{n=1}^{\infty} n(2x)^{n+1} = \frac{(2x)^2}{(1-2x)^2} \implies \sum_{n=1}^{\infty} n 2^{n-1} x^{n+1} = \frac{x^2}{(1-2x)^2}, ~ |x| < \tfrac{1}{2}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: September 29th 2010, 07:11 AM
  2. Replies: 0
    Last Post: January 26th 2010, 09:06 AM
  3. Formal power series & Taylor series
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: April 19th 2009, 10:01 AM
  4. Multiplying power series - Maclaurin series
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 8th 2009, 12:24 AM
  5. Replies: 10
    Last Post: April 18th 2008, 11:35 PM

Search Tags


/mathhelpforum @mathhelpforum