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!

Formula for the alternating sum of the first n numbers.

  1. Jul 22, 2011 #1
    1. The problem statement, all variables and given/known data
    The alternating sum of the first five numbers is 1-2+3-4+5=3. Find a formula for the alternating sum of the first n numbers. How about the alternating sum of the squares of the first n numbers?


    2. Relevant equations

    Sum of the first n numbers. [itex]\frac{n(n+1)}{2}[/itex]

    Sum of the first n even numbers. n(n+1)

    Sum of the first n odd numbers. n2

    3. The attempt at a solution

    Sum of the first n alternating numbers if n is odd. [itex]{(\frac{n+1}{2}})^{2}-(\frac{n-1}{2})({\frac{n-1}{2}+1})[/itex]

    Sum of the first n alternating numbers if n is even. [itex]{(\frac{n}{2}})^{2}-(\frac{n}{2})({\frac{n}{2}+1})[/itex]

    I cannot figure out how to combine these two equations into one that will work for both odd and even n. I have not even begun the second part of the problem.
     
  2. jcsd
  3. Jul 22, 2011 #2
    Maybe you should consider the first few partial sums of the alternating series and find a formula from that.
     
  4. Jul 22, 2011 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Do you know the formula for Sn(x) = sum{x^k,j=1..n}? Have you looked at the summation for Tn(x) = x*dSn(x)/dx? Can you see how to continue from there?

    RGV
     
  5. Jul 22, 2011 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Two excellent resposes.

    (Darn, leave me nothing to say.)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Formula for the alternating sum of the first n numbers.
Loading...