Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n. is divisible by 2

Question

What will be an ideal response?

Answer 1

First, we show that the statement is true when n = 1.
For 
This is a true statement and Condition I is satisfied.

Next, we assume the statement holds for some k. That is,
  is divisible by 2 is true for some positive integer k.
We need to show that the statement holds for . That is, we need to show that 
   is divisible by 2.

So we assume  is divisible by 2 and look at the expression for n = k + 1.
 

Since  is divisible by 2, then  for some integer m. Hence,
 

Condition II is satisfied. As a result, the statement is true for all natural numbers n.