Results 1 to 2 of 2

Math Help - Help with summations.

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    69

    Help with summations.

    Hello, I am having trouble solving this summation:

    Summation from j=i to N-1 of: (j-i+1)

    The answer is said to be: ((N-i+1)(N-i)) / 2

    I have tried separating the summation into three separate summations consisting of:
    (summation from j=i to N-1 of j) - (summation from j=i to N-1 of i) + (summation from j=i to N-1 of 1)
    This leads me to: ((N+2)(N-1) / 2) - i(N-i-1)
    But that is obviously not the right answer (unless I am simplifying something incorrectly). Please let me know what I am doing wrong. I have been stuck on this problem for a while now and I need to move on with my homework. Thank you very much for your help.
    Last edited by mr fantastic; January 25th 2011 at 11:53 AM. Reason: Title.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Failure's Avatar
    Joined
    Jul 2009
    From
    Zürich
    Posts
    555
    Quote Originally Posted by collegestudent321 View Post
    Hello, I am having trouble solving this summation:

    Summation from j=i to N-1 of: (j-i+1)

    The answer is said to be: ((N-i+1)(N-i)) / 2

    I have tried separating the summation into three separate summations consisting of:
    (summation from j=i to N-1 of j) - (summation from j=i to N-1 of i) + (summation from j=i to N-1 of 1)
    This leads me to: ((N+2)(N-1) / 2) - i(N-i-1)
    But that is obviously not the right answer (unless I am simplifying something incorrectly). Please let me know what I am doing wrong. I have been stuck on this problem for a while now and I need to move on with my homework. Thank you very much for your help.
    Well, it's an arithmetic series having (N-1)-i+1=N-i terms (assuming that i\leq N-1). Therefore, summing the series can be done by multiplying the average of the first and last term by the number of terms. This gives

    \frac{(i-i+1)+(N-1-i+1)}{2}\cdot (N-i)=\frac{(N-i+1)\cdot (N-i)}{2}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Summations
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: December 6th 2010, 07:22 AM
  2. summations
    Posted in the Algebra Forum
    Replies: 5
    Last Post: September 27th 2010, 04:23 AM
  3. Summations please help!!!
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: November 15th 2009, 01:01 AM
  4. summations
    Posted in the Algebra Forum
    Replies: 6
    Last Post: December 16th 2008, 01:41 PM
  5. Summations
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 26th 2008, 11:37 AM

Search Tags


/mathhelpforum @mathhelpforum