Proof by mathematical induction

Question 1

Explain how proof by induction works

Answer 1

First, the base case is proven by simply showing that when n equals a certain value (typically 1), the statement holds. Then, an assumption is made that the statement holds when n equals any k. From this assumption, we now prove that if the statement holds when n=k, then it also holds when n=k+1. As we have shown that the statement holds for n=1, it must also hold for n=2, n=3, and so on