Step-by-step explanation:
We will prove by mathematical induction that, for every natural n,
We will prove our base case (when n=1) to be true:
Base case:
Inductive hypothesis:
Given a natural n,
Now, we will assume the inductive hypothesis and then use this assumption, involving n, to prove the statement for n + 1.
Inductive step:
Observe that, for y=0 the conclusion is clear. Then we will assume that
With this we have proved our statement to be true for n+1.
In conlusion, for every natural n,