1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding the Sum of a Power Series

  1. Nov 27, 2006 #1
    I'm trying to find the sum of this:

    [tex]
    \[
    \sum\limits_{n = 0}^\infty {( - 1)^n nx^n }
    \]
    [/tex]

    This is what I have so far:

    [tex]
    \[
    \begin{array}{l}
    \frac{1}{{1 - x}} = \sum\limits_{n = 0}^\infty {x^n } \\
    \frac{1}{{(1 - x)^2 }} = \sum\limits_{n = 0}^\infty {nx^{n - 1} } = \sum\limits_{n = 1}^\infty {nx^{n - 1} } \\
    \frac{x}{{(1 - x)^2 }} = \sum\limits_{n = 1}^\infty {nx^n } \\
    \end{array}
    \]
    [/tex]

    So how do I get the (-1)^n part in there? Any suggestions would be really helpful. Thanks.
     
  2. jcsd
  3. Nov 27, 2006 #2
    [tex] \frac{1}{1+x} = \sum_{n=0}^{\infty} (-1)^{n}x^{n} [/tex]
     
    Last edited: Nov 27, 2006
  4. Nov 27, 2006 #3
    Oh, I see.. Where exactly does that come from?
     
  5. Nov 27, 2006 #4
    [tex] \frac{1}{1+x} = \frac{1}{1-(-x)} = \sum_{n=0}^{\infty} (-x)^{n} = (-1)^{n}x^{n} [/tex]
     
  6. Nov 27, 2006 #5
    Ah! Of course. Okay. Thanks.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Finding the Sum of a Power Series
  1. Sum of a power series (Replies: 9)

Loading...