Results 1 to 3 of 3

Math Help - Infinite series

  1. #1
    Newbie
    Joined
    Mar 2012
    From
    Australia
    Posts
    11

    Infinite series

    Hi, just wondering if anyone can help me with a quick infinite series question:
    Show that this series diverges: \sum_{n=1}^{\infty }\frac{2}{n}-\frac{1}{2^n}
    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,407
    Thanks
    1294

    Re: Infinite series

    Quote Originally Posted by Dragonkiller View Post
    Hi, just wondering if anyone can help me with a quick infinite series question:
    Show that this series diverges: \sum_{n=1}^{\infty }\frac{2}{n}-\frac{1}{2^n}
    Thanks
    The Harmonic Series is divergent...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,412
    Thanks
    1328

    Re: Infinite series

    You know, or should know, that \sum \frac{1}{2^n} converges- it is a geometric series and there is a simple formula for its sum.
    IF the given sum converged, then we could write 2\sum\frac{1}{n}= \sum\left(\frac{2}{n}- \frac{1}{2^n}\right)+ \sum \frac{1}{2^n} but, as Prove It said, the series on the left does not converge.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Fourier series to calculate an infinite series
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: August 4th 2010, 01:49 PM
  2. Replies: 2
    Last Post: May 26th 2010, 09:17 AM
  3. Replies: 7
    Last Post: October 12th 2009, 10:10 AM
  4. Replies: 2
    Last Post: September 16th 2009, 07:56 AM
  5. Replies: 1
    Last Post: May 5th 2008, 09:44 PM

Search Tags


/mathhelpforum @mathhelpforum