Question

prove that n^2-n for every positive integer n

Answer 1

Step-by-step explanation:

Let P(n) : 2 > for all positive n For n = 1 L.H.S = 2 = 2 1 = 1 R.H.S = n = 1 Since 2 > 1 L.H.S > R.H.S ∴ P(n) is true for n = 1. Assume that P(k) is true for all positive integers k i.e. 2 k > k We will prove that P(k + 1) is true. i.e 2 + 1 > k + 1 From (1) 2 k > k Multiplying by 2 on both sides.