Course: Foundations of Higher MAth

Prove that for every positive integer n.

This is a question from my final exam today.

P(n):

P(1): is a true statement.

Assume P(k) is true. Then for some integer a.

Then

P(k+1):

Therefore, . By PMI, P(n) is true for every positive integer n.

None of my friends used this method though. Is this a correct way to do it?