Question: prove by induction 7 n 2 n is divisible by 5?
Answer: Let P(n): 7n – 2n is divisible by 5, for any natural number n. ... = 5(7k + 2m), which divisible by 5. Thus, P(k + 1) is true whenever P(k) is true. So, by the principle of mathematical induction P(n) is true for all natural numbers n.