Question

1. Use principle of mathematical induction to prove that n²-7n+3 is divisible by 3 for all natural numbers n.​

Answer 1

Explanation:

Answer. Let P(n): n3 – 7n + 3 is divisible by 3, for all natural numbers n. ... = 3[m + (k(k + 1) – 2)], which is divisible by 3 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.