Simplify the fraction

Question

I want to simplify this fraction

$ \frac {1+a+a^2+...+a^n}{1+a^{-1}+a^{-2}+...+a^{-n}} $ where, $ a \in {\mathbb R^*} $ and $ n \in {\mathbb N^*} $

I think is some kind of formula here

Answer 1

You didn't really have to use the geometric progression here (though that might help too). Just multiply the denominator by $a^n$ and see what happens.