Results 1 to 5 of 5

Math Help - Show how two series as the same Sum

  1. #1
    Newbie
    Joined
    Jun 2010
    Posts
    10

    Question Show how two series as the same Sum

    show that the sum of the first 2n terms of the series 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5........................is the same as the sum of the first n terms of the series 1/1*2 + 1/2*3 + 1/3*4 +1/4*5................... Do these series converge? what is the sum of the first 2n+1 terms of the first series and how to get the sum?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Nov 2009
    Posts
    130
    (1) Hint: 1+(-1/2+1/2)+(-1/3+1/3)+(-1/4+1/4)+(-1/5+1/5)+...+(-1/(2n) + 1/(2n))
    (2) Hint: 1/(1*2) + 1/(2*3) + 1/(3*4) +1/(4*5) + ... + 1/(n*(n+1))
    1/(n*(n+1)) = 1/n - 1/(n+1)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    May 2010
    Posts
    98
    The first one obviously converges to 1. 1+(\frac{-1}{2}+\frac{1}{2})+(\frac{-1}{3}+\frac{1}{3})+... since (\frac{-1}{2}+\frac{1}{2})=0 they eliminate eachother.

    The second is \sum_{1}^{n}\frac{n}{n(n+1)}=\sum_{1}^{n}\frac{1}{  n}-\frac{1}{n+1} =(\frac{1}{1}-\frac{1}{2})+(\frac{1}{2}-\frac{1}{3})+...=1+(\frac{-1}{2}+\frac{1}{2})+(\frac{-1}{3}+\frac{1}{3})+...=1
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jun 2010
    Posts
    10
    thank u guys i was mistaken 2n a 2xSn=2x(1+1/2-1/2......
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    May 2010
    Posts
    98
    Oh, i missed the 2n, but the argument would be very similar, use p0oints hints
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: October 3rd 2011, 01:12 AM
  2. show this series diverge
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: July 4th 2009, 10:29 AM
  3. how to show this series uni. convergent
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: May 9th 2009, 05:50 PM
  4. Replies: 3
    Last Post: May 4th 2009, 03:58 PM
  5. Show a series converges for any x
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 24th 2006, 11:29 PM

Search Tags


/mathhelpforum @mathhelpforum