A student was asked to prove a statement by induction. He proved
i) P(5) is true and
ii) truth of P(n) truth of P(n+1), .
On the basis of this, he could conclude that P(n) is true

Hint:

Consider a statement P(n), where n is a natural number. Then to determine the validity of P(n) for every n, use the following principle:
Step 1:  Check whether the given statement is true for n = 1.
Step 2: Assume that given statement P(n) is also true for n = k, where k is any positive integer.
Step 3:  Prove that the result is true for P(k+1) for any positive integer k.
If the above-mentioned conditions are satisfied, then it can be concluded that P(n) is true for all n natural numbers.