Results 1 to 6 of 6

Math Help - Summation problem __

  1. #1
    Newbie
    Joined
    Oct 2010
    Posts
    10

    Summation problem __

    Knowing that 1/(1-x) = Σ x^n , for n=0 to inf.
    Can anyone help me to find a power series summation rule for the function 1/(1-x^2) .

    And also for which values does it converge ?

    Thanks in advance
    Nikolas
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1
    Quote Originally Posted by tsebamm View Post
    Knowing that 1/(1-x) = Σ x^n , for n=0 to inf.
    Can anyone help me to find a power series summation rule for the function 1/(1-x^2) .

    And also for which values does it converge ?

    Thanks in advance
    Nikolas
    \sum_{n=0}^{\infty}x^{2n}  <br />
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2010
    Posts
    10
    Quote Originally Posted by Also sprach Zarathustra View Post
    \sum_{n=0}^{\infty}x^{2n}  <br />
    thanks for your quick reply. Can you explain a bit your answer?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Mar 2010
    Posts
    715
    Thanks
    2
    You know that \frac{1}{1-t} = \sum_{n=0}^{\infty}t^n. If t = x^2, then \frac{1}{1-x^2} =  \sum_{n=0}^{\infty}(x^2)^n = \sum_{n=0}^{\infty}{x}^{2n}.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Oct 2010
    Posts
    10
    Quote Originally Posted by TheCoffeeMachine View Post
    You know that \frac{1}{1-t} = \sum_{n=0}^{\infty}t^n. If t = x^2, then \frac{1}{1-x^2} =  \sum_{n=0}^{\infty}(x^2)^n = \sum_{n=0}^{\infty}{x}^{2n}.
    I proved it about an hour ago. Thanks anyway!
    Cheers!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Now-value? Summation problem.
    Posted in the Business Math Forum
    Replies: 2
    Last Post: May 11th 2011, 03:33 AM
  2. Summation Problem
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: December 29th 2010, 03:23 PM
  3. summation problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 1st 2010, 01:26 PM
  4. summation problem
    Posted in the Pre-Calculus Forum
    Replies: 22
    Last Post: November 7th 2009, 11:09 PM
  5. Summation Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 26th 2007, 07:32 PM

Search Tags


/mathhelpforum @mathhelpforum