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Determine the following sum,,

  1. Apr 30, 2009 #1
    1. The problem statement, all variables and given/known data
    hi guys ,, i hope you all are fine ,,
    i have a problem with this question :
    Determine the following sum:
    1-4+9-16+25-...-10000+10201

    2. Relevant equations



    3. The attempt at a solution
    i don't know where even to start ,, can anyone give me an idea how to solve problems like these ??
     
  2. jcsd
  3. Apr 30, 2009 #2
    Do you see a pattern between the numbers? Try to write it in summation form i.e. [tex] \sum_{i=1}^n \left\{... \right\}[/tex]; after you see the pattern, you should know what n is. Then you can find the sum.
     
  4. Apr 30, 2009 #3
    i got an idea that Sum (1,51) (2x-1)^2-(2x-2)^2 = 5151
    is it right ??
     
  5. Apr 30, 2009 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    The number is right. If you are clear how to get it from your expression, you should be ok.
     
  6. Apr 30, 2009 #5
    thanks very much :D , i just needed to be sure of my way
     
  7. May 2, 2009 #6
    You're wasting your time: That series does not and cannot converge. How could it? The terms get bigger and bigger.

    Read up on what it means for an infinite series to converge.
     
  8. May 2, 2009 #7
    No, you're wrong there's no infinite series.

    Maybe YOU should read better.
     
  9. May 2, 2009 #8

    Mark44

    Staff: Mentor

    As Dirk pointed out, and as you can see in the OP, this is a finite sum.
     
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