Hi

The idea behind what you use is a non-inductive proof, which is:

Let be an integer, (the equivalence is true because n positive integer). Since we assumed we have what we want.

In a usual proof by induction, you assume your induction hypothesis (case ) and try to show the statement forusing the case

So for your proof, writing is a good thing. What you have to do now is to obtain using the induction hypothesis: