Results 1 to 2 of 2

Math Help - Solving an infinite series that doesn't seem to be harmonic or geometric

  1. #1
    Newbie
    Joined
    Nov 2010
    Posts
    1

    Solving an infinite series that doesn't seem to be harmonic or geometric

    I'm solving a visual problem, and sparing the boring details, I've found the sequence to be:

    {a_n} = \frac{1}{2^{2n-1}}

    I need to solve for the sum of the series from 1 to infinity. Wolfram easily solves this as 2/3. However, I've poured over 2 calculus books and I've enlisted help but we can't solve it by hand.

    \displaystyle\sum_{n=1}^{\infty}\frac{1}{2^{2n-1}}

    Any help at simplifying this into a series which I can solve would be greatly appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,061
    Thanks
    900
    Quote Originally Posted by funnyguy View Post
    I'm solving a visual problem, and sparing the boring details, I've found the sequence to be:

    {a_n} = \frac{1}{2^{2n-1}}

    I need to solve for the sum of the series from 1 to infinity. Wolfram easily solves this as 2/3. However, I've poured over 2 calculus books and I've enlisted help but we can't solve it by hand.

    \displaystyle\sum_{n=1}^{\infty}\frac{1}{2^{2n-1}}

    Any help at simplifying this into a series which I can solve would be greatly appreciated.
    \displaystyle \frac{1}{2^{2n-1}} = 2^{1-2n} = \frac{2}{2^{2n}} = \frac{2}{4^n}

    \displaystyle 2 \sum_{n=1}^{\infty} \frac{1}{4^n} = 2 \cdot \frac{\frac{1}{4}}{1 - \frac{1}{4}} = 2 \cdot \frac{1}{3} = \frac{2}{3}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Infinite Geometric Series
    Posted in the Pre-Calculus Forum
    Replies: 12
    Last Post: May 10th 2010, 06:17 AM
  2. Infinite series of geometric?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 12th 2010, 05:51 PM
  3. Infinite geometric series
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: April 12th 2010, 03:15 PM
  4. Infinite Sum of a Geometric Series
    Posted in the Calculus Forum
    Replies: 4
    Last Post: February 23rd 2010, 04:40 PM
  5. Infinite & Geometric Series
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 17th 2009, 10:18 PM

Search Tags


/mathhelpforum @mathhelpforum