- #1
jegues
- 1,097
- 3
Homework Statement
I'm having some confusion about combining sums. Our goal when combining these sums is to have the,
[tex](x-c)^{\text{whatever}}[/tex]
term to be the same in both sums.
My confusion is better explained in an example. (see below)
Homework Equations
The Attempt at a Solution
Let's say we have the following 2 sums and we want to simplify them into one sum,
[tex]\sum_{n=0}^{\infty} (-1)^{n}2^{n}nx^{n+1} + \sum_{n=0}^{\infty} (-1)^{n}2^{n}nx^{n-1}[/tex]
As you can see the,
[tex](x-c)^{\text{whatever}}[/tex]
terms are not identical, one is (n+1) and the other is (n-1).
So if we wanted to make the two exponents identical for the first sum we would look as,
[tex]n \rightarrow n-1[/tex],
and plug in (n-1) where all the n's used to be in the first sum, and change the starting point of the sum to 1
Now for the second sum, we would look as,
[tex]n \rightarrow (n+1)[/tex],
and plug in (n+1) where all the n's used to be in the second sum,
***Here's where I get confused***
But my professor had mentioned to the class that this would not change the starting point of the sum to n= -1, it stays at n=0.
Why is that? Can someone please clarify?
Thanks again!