I'm not quite sure what you're doing...? It almost looks like you've assumed the k+1 step, and then did something to it, like working backwards...?
First, you need to show that the equation is true for n = 1.
Once you've done that, assume that the equation is true for some n = k:
You then do the k+1-th step for the left-hand side, and see where that leads:
Now substitute from the assumption step:
Convert to a common denominator, combine the terms, and see what you get. It might help to note that you're wanting eventually to end up with: