Results 1 to 1 of 1

Math Help - Summing an Infinite Series

  1. #1
    Junior Member
    Joined
    Jan 2009
    Posts
    25

    Summing an Infinite Series

    Hello. I'm stuck on another proof. Can anyone help me with this problem?

    Let S of N be the Nth partial sum of the harmonic series

    \sum_{n=1}^{\infty}\frac{1}{n}

    a) Verify the following inequality for n=1,2,3. Then prove it for general n.

    \frac{1}{2^{n-1} + 2} + \frac{1}{2^{n-1} + 1} + \frac{1}{2^{n-1} + 3} + ... + \frac{1}{2^n} \leq \frac{1}{2}


    b) Prove that S diverges by showing that S of N \leq 1+\frac{n}{2} for N= 2^{n}

    Hint: Break up Sn into n+1 sums of length 1,2,4,8..., as in the following:

    S of 2^{3} = 1 + (1/2) + (1/3 + 1/4) + (1/5 + 1/6 + 1/7 + 1/8)



    Thank you!
    Last edited by wyhwang7; February 20th 2009 at 12:58 AM. Reason: Corrections to the problem
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Summing Infinite Series Questions
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: August 30th 2010, 11:10 AM
  2. Summing a series problem
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: March 1st 2010, 05:49 AM
  3. Summing a complex series
    Posted in the Algebra Forum
    Replies: 9
    Last Post: September 8th 2009, 07:00 AM
  4. summing series
    Posted in the Calculus Forum
    Replies: 0
    Last Post: December 1st 2006, 05:38 AM
  5. Summing a series.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 25th 2005, 07:24 AM

Search Tags


/mathhelpforum @mathhelpforum