Results 1 to 3 of 3

Math Help - representing function as power serries

  1. #1
    Senior Member
    Joined
    Jun 2009
    Posts
    251

    representing function as power serries

    question: f(x)=\frac{1}{x-5}
    answer: -\sum_{n=0}^\infty \frac{1}{5^{n+1}}x^n for |x|<5
    work: \frac{1}{x-5}=\frac{1}{-5} \times \frac{1}{1-x} \longrightarrow \frac{1}{-5} \sum_{n=0}^\infty x^n
    Last edited by superdude; August 3rd 2009 at 01:41 PM. Reason: improved redability
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    14
    \frac{1}{x-5}=-\frac{1}{5}\cdot \frac{1}{1-\frac{x}{5}}=-\frac{1}{5}\sum\limits_{n=0}^{\infty }{\left( \frac{x}{5} \right)^{n}}=-\sum\limits_{n=0}^{\infty }{\frac{x^{n}}{5^{n+1}}}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member DeMath's Avatar
    Joined
    Nov 2008
    From
    Moscow
    Posts
    473
    Thanks
    5
    Quote Originally Posted by superdude View Post
    question: f(x)=\frac{1}{x-5}
    answer: -\sum_{n=0}^\infty \frac{1}{5^{n+1}}x^n for |x|<5
    work: \frac{1}{x-5}={\color{red}{\frac{1}{-5} \times \frac{1}{1-x} \longrightarrow \frac{1}{-5} \sum_{n=0}^\infty x^n}}
    f\left( x \right) = \frac{1}{{x - 5}} =  - \frac{1}{{5 - x}} =  - \frac{1}{5} \cdot \frac{1}{{1 - \left( {{x \mathord{\left/{\vphantom {x 5}} \right.\kern-\nulldelimiterspace} 5}} \right)}} =

    =  - \frac{1}{5}\left( {1 + \frac{x}{5} + \frac{{{x^2}}}{{25}} +  \ldots  + \frac{{{x^n}}}{{{5^n}}} +  \ldots } \right) =

    - \frac{1}{5}\sum\limits_{n = 0}^\infty  {\frac{{{x^n}}}{{{5^n}}}}  =  - \sum\limits_{n = 0}^\infty  {\frac{{{x^n}}}{{{5^{n + 1}}}}} ,{\text{ }}\left| x \right| < 5.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] An expression representing the following function...
    Posted in the Pre-Calculus Forum
    Replies: 7
    Last Post: September 24th 2010, 08:50 PM
  2. Representing functions as Power Series
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 16th 2009, 04:18 PM
  3. alternating serries test
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 1st 2009, 11:55 PM
  4. converging serries
    Posted in the Calculus Forum
    Replies: 6
    Last Post: July 27th 2009, 01:40 AM
  5. Fourier Serries - Integration Help
    Posted in the Calculus Forum
    Replies: 10
    Last Post: May 30th 2007, 04:15 PM

Search Tags


/mathhelpforum @mathhelpforum