The problem statement, all variables and given/known data

I'm having some confusion about combining sums. Our goal when combining these sums is to have the,

term to be the same in both sums.

My confusion is better explained in an example. (see below)

The attempt at a solution

Let's say we have the following 2 sums and we want to simplify them into one sum,

As you can see the,

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,

,

and plug in (n-1) where all the n's used to be in the first sum, andchange the starting point of the sum to 1

Now for the second sum, we would look as,

,

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!