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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


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    Staff Emeritus
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    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.
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