Question

Prove by using principle of Induction.41n–14n is divisible by 27.

Answer 1

Let the given statement be P(n), i.e., P(n):41n – 14nis a multiple of 27. It can be observed that P(n) is true for n = 1 since 411−141 =27 41 1 - 14 1 = 27 , which is a multiple of 27. ... Hence, by the principle of mathematical induction, statement P(n) is true for all natural numbers i.e., n.