# Changing variable in a sumation

1. Oct 19, 2007

### wildman

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:
$$\sum_{k=n+1}^{0} -k 3^k$$

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

$$\sum_{m=0}^{-n-1} m (\frac{1}{3})^m$$

3. The attempt at a solution

I can see where the $$m (\frac{1}{3})^m$$ came from (just stick -m in for the k), but how did the summation change?

2. Oct 19, 2007

### cristo

Staff Emeritus
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.

3. Oct 19, 2007

### wildman

That much is obvious, but why is the 0 on the bottom and the -n-1 on the top now?

4. Oct 20, 2007

### wildman

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.