Results 1 to 6 of 6

Math Help - Power series representatin of a function

  1. #1
    Junior Member
    Joined
    May 2009
    Posts
    53

    Power series representatin of a function

    Question:

    Find a power series representation for the function.

    f(x) = \frac{3}{1-x^2}

    My solution:

    Since, \frac{1}{1-x} = 1 + x + x^2 + x^3 + .... = \sum_{n=0}^{\infty} x^n

    Then,

     <br />
\frac{3}{1-x^2} = \sum_{n=0}^{\infty} 3x^{2n}<br />

    Am I correct?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,114
    Thanks
    988
    Quote Originally Posted by calc101 View Post
    Question:

    Find a power series representation for the function.

    f(x) = \frac{3}{1-x^2}

    My solution:

    Since, \frac{1}{1-x} = 1 + x + x^2 + x^3 + .... = \sum_{n=0}^{\infty} x^n

    Then,

     <br />
\frac{3}{1-x^2} = \sum_{n=0}^{\infty} 3x^{2n}<br />

    Am I correct?
    looks fine.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    May 2009
    Posts
    53
    And I calculated the radius of convergence to be: 1, with the following interval: (-1,1). Correct?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member DeMath's Avatar
    Joined
    Nov 2008
    From
    Moscow
    Posts
    473
    Thanks
    5
    Quote Originally Posted by calc101 View Post
    Question:

    Find a power series representation for the function.

    f(x) = \frac{3}{1-x^2}

    My solution:

    Since, \frac{1}{1-x} = 1 + x + x^2 + x^3 + .... = \sum_{n=0}^{\infty} x^n

    Then,

     <br />
\frac{3}{1-x^2} = \sum_{n=0}^{\infty} 3x^{2n}<br />

    Am I correct?
    Sorry!
    Last edited by DeMath; July 17th 2009 at 11:03 AM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor Bruno J.'s Avatar
    Joined
    Jun 2009
    From
    Canada
    Posts
    1,266
    Thanks
    1
    Awards
    1
    Quote Originally Posted by DeMath View Post
    A small clarification: for  x \in \left( { - \infty ;{\text{ }} - 1} \right) \cup \left( { - 1;{\text{ }}1} \right) \cup \left( {1;{\text{ }}\infty } \right).
    Are you saying for example that \frac{3}{1-2^2}=3\sum_{j=1}^\infty2^{2j}?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,961
    Thanks
    1784
    Awards
    1
    Quote Originally Posted by calc101 View Post
    And I calculated the radius of convergence to be: 1, with the following interval: (-1,1). Correct?
    Yes this correct.

    Whereas
    Quote Originally Posted by DeMath View Post
    A small clarification: for  x \in \left( { - \infty ;{\text{ }} - 1} \right) \cup \left( { - 1;{\text{ }}1} \right) \cup \left( {1;{\text{ }}\infty } \right).
    Is grossly misguided!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. find the power series for the function....
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 13th 2010, 08:07 AM
  2. Power Series&Function Series Questions
    Posted in the Calculus Forum
    Replies: 10
    Last Post: January 20th 2010, 12:38 AM
  3. power series representation of a function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 12th 2009, 04:00 PM
  4. Power series representation of a function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 12th 2009, 02:35 PM
  5. write a function as a power series
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 22nd 2008, 01:56 AM

Search Tags


/mathhelpforum @mathhelpforum