Results 1 to 6 of 6

Math Help - Finding power series for given values of a sum

  1. #1
    Member
    Joined
    May 2010
    Posts
    241

    Finding power series for given values of a sum

    I have this exercise which I'm not sure how to solve.
    It says: Consider the series \displaystyle\sum_{n=0}^{\infty}x^n Does exists any value of x for which the series converges to five? żand to 1/3?

    Well, I've reasoned that if there exists that value, then it must be inside of the radius of convergence for the series. So I've found the radius of convergence:

    a_n=1

    R=\displaystyle\lim_{n \to{}\infty}{\left |{\displaystyle\frac{a_n}{a_{n+1}}}\right |}=1

    But now I don't know how to proceed.
    Last edited by Ulysses; April 29th 2011 at 12:44 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member girdav's Avatar
    Joined
    Jul 2009
    From
    Rouen, France
    Posts
    678
    Thanks
    32
    Did you try to compute the sum?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    May 2010
    Posts
    241
    I'll try.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    19,202
    Thanks
    1880
    Awards
    1
    Quote Originally Posted by Ulysses View Post
    I have this exercise which I'm not sure how to solve. It says: Consider the series \displaystyle\sum_{0}^{\infty}x^n Does exists any value of x for which the series converges to five? żand to 1/3?
    Hint. If the series converges \sum\limits_{n = 0}^\infty  {x^n }  = \frac{1}{{1 - x}}.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,304
    Thanks
    447
    Awards
    1
    Quote Originally Posted by Ulysses View Post
    \displaystyle\sum_{0}^{\infty}x^n
    Just as a side note for notation... I doubt anyone seriously thinks that this sum is over x. However you have not specified that. Here is the code to make this a sum over n from 0 to infinity:
    \displaystyle\sum_{n = 0}^{\infty}x^n

    -Dan
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    6
    Finding the sum of the 'geometric series'...



    ... is based on the 'algebraic identity'...

    (1)

    ... from which follows...

    (2)

    ... so that if |x|<1 is...

    (3)

    Kind regards

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding a power series
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 6th 2010, 07:41 AM
  2. finding values from power functions
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 7th 2008, 12:52 PM
  3. finding values from power functions
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 6th 2008, 08:51 PM
  4. Help finding a power series
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 29th 2008, 04:26 PM
  5. Replies: 10
    Last Post: April 18th 2008, 10:35 PM

Search Tags


/mathhelpforum @mathhelpforum