There are a couple of problems with your post. Firstly I don't believe that formula is correct. According to your formula the LHS when n=1 is
I believe what you should be trying to prove is
Secondly your approach for taking the inductive step seems a little strange- in such proofs you prove the base case (i.e. n=1) and then assume the formula to be true for n=1,..,k. Then you consider the LHS when n=k+1, and use the fact that
to prove the formula for all n.
I hope this helps.