Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Changing variable in a sumation

  1. Oct 19, 2007 #1
    1. The problem statement, all variables and given/known data
    I have been shown this manipulation of a summation and I am wondering why the person could do it:
    [tex] \sum_{k=n+1}^{0} -k 3^k [/tex]

    Now change the variables with m=-k and we get:

    [tex] \sum_{m=0}^{-n-1} m (\frac{1}{3})^m[/tex]

    3. The attempt at a solution

    I can see where the [tex] m (\frac{1}{3})^m[/tex] came from (just stick -m in for the k), but how did the summation change?
  2. jcsd
  3. Oct 19, 2007 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    Well, k=n+1 corresponds to m=-k=-n-1, and k=0 corresponds to m=0, so the new limits are m=0, m=-n-1.
  4. Oct 19, 2007 #3
    That much is obvious, but why is the 0 on the bottom and the -n-1 on the top now?
  5. Oct 20, 2007 #4
    Never mind, that question is obvious also. Of course if you change the sign you would have to move the values on the summation.... Problem solved.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook