The way you have written it both are the same. So I have changed it. See the above part marked in red.

Yes both are correct. That happens because .

Lets use it and prove that:

Now put t = n - k, the k varies from 0 to n, t varies from n to 0(thats the same as 0 to n).

But het t is just a variable we introduced to count the powers of a, its a dummy variable. Lets replace it with k.

Hence proved