Results 1 to 3 of 3

Math Help - Sequence and series

  1. #1
    Member roshanhero's Avatar
    Joined
    Aug 2008
    Posts
    176

    Sequence and series

    How to do this?
    \sum_{k=1}^{100}(-1)^{k}k
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Aug 2009
    From
    Mumbai
    Posts
    83
    Sum = -1+2-3+4+........-99+100

    =(2-1) + (4-3) +......+(100-99)
    =1+1+1+.....+1(50 times)
    =50??
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by roshanhero View Post
    How to do this?
    \sum_{k=1}^{100}(-1)^{k}k
    To make a little clearer, just like bandekrait did, note that \sum_{\ell=1}^{100}(-1)^{\ell}\ell=\sum_{\ell=1}^{50}(-1)^{2\ell+1}(2\ell-1)+\sum_{\ell=1}^{50}(-1)^{2\ell}2\ell (the evens in the odds) but (-1)^{2\ell-1}=-1,(-1)^{2\ell}=1 so this becomes \sum_{\ell=1}^{50}-\left\{2\ell-1\right\}+\sum_{\ell=1}^{50}2\ell=\sum_{\ell=1}^{5  0}1=50.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. sequence series
    Posted in the Algebra Forum
    Replies: 5
    Last Post: November 5th 2010, 04:45 AM
  2. sequence and series
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 6th 2008, 06:48 PM
  3. more sequence/series
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 24th 2008, 09:13 AM
  4. Replies: 11
    Last Post: April 1st 2008, 12:06 PM
  5. Replies: 2
    Last Post: January 23rd 2007, 08:47 AM

Search Tags


/mathhelpforum @mathhelpforum