finding number of terms in a series?

[fkkiwi]

I'm really confused as to how the number of terms here is "n - r + 1"

[jazcstuart]

I'm really confused as to how the number of terms here is "n - r + 1"

You have every power of r to n inclusive, therefore the number of terms is n-r+1 (because you have every number between n and r, n-r, plus the first term (1+x)^r).
Imagine if n=10 and r=0. 10-0 means you have every power from 1 to 10, but you also have to include r=0.
Sorry that was a confusing explanation, but hope it makes sense.