Prove by induction that $sum_{i=0}^n left(frac 3 2 right)^i = 2left(frac 3 2 right)^{n+1} -2$

Prove, disprove, or give a counterexample:

$$\sum_{i=0}^n \left(\frac 3 2 \right)^i = 2\left(\frac 3 2 \right)^{n+1} -2.$$

I went about this as a proof by induction. I did the base case and got the LHS = RHS. When I went to show $P(k) \implies P(k+1)$ I could not get the LHS to equal the RHS. Is this because it isn't a proof by induction? Or, that it cannot be proved?

Any help would be greatly appreciated.