Solve easy sums with Binomial Coefficient How do we get to the following results:
$$\sum_{i=0}^n 2^{-i} {n \choose i} = \left(\frac{3}{2}\right)^n$$
and 
$$\sum_{i=0}^n 2^{-3i} {n \choose i} = \left(\frac{9}{8}\right)^n.$$
I guess I could prove it by induction. But is there an easy way to derive it?
Thank you very much.

For the first one consider the binomial expansion of $(1+\frac{1}{2})^n$ and see how close that is the left hand side while adding the values will give the right hand side.
For the second, consider putting in $\frac{1}{8}$ and note what fraction is 2 to the negative 3.
