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Homework Help: Rewrite an even of N series as a function of N

  1. Oct 9, 2015 #1
    1. The problem statement, all variables and given/known data
    If N is even, so that 1+2+3+...+N = (N+1)N/2

    2. Relevant equations

    3. The attempt at a solution
    I can easily rewrite the summation as Screenshot (2).png but I do not know how to justify the question. Thank you.
  2. jcsd
  3. Oct 9, 2015 #2


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    This is not the way to rewrite that summation. It should be ##\sum_{x=1}^N{x}##. Your sum just gives ##N##.

    Can you see a way to group the first and the last term together, then the second and the next to last, etc..?
  4. Oct 9, 2015 #3
    I see... If I take N = 4, the it will be 1+2+3+4 = 10
    I can group them into (1+4) + (2+3) = 5 + 5. So there are two terms, so 4/2

    If N =6 then it will be 1+2+3+4+5+6= 21
    and I can group them into (1+6) + (2+5) +(3+4) = 7+7+7, so there are 3 terms, so 6/2

    So it looks like the general formula, if N is even, is (N/2)(N+1)
    Now I get it!
    Thank you!
  5. Oct 9, 2015 #4


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    Maybe I should have added that it is not necessary to suppose that ##N## is even. The "grouping" trick works generally.
  6. Oct 9, 2015 #5


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    I see that lately you haven't posted here very much.

    As a reminder, please state your complete problem in the body of your thread, no mater what is stated in the title.

    It's not at all clear, what you're trying to do here.
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