1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
    n/a

    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

    Krylov

    User Avatar
    Science Advisor
    Education Advisor

    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

    Krylov

    User Avatar
    Science Advisor
    Education Advisor

    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

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted