Question

If p(n) : n2 > 100 then

(A) p(1) is true

(B) p(4) is true

(C) p(k) is true k ≥ 5, k ∈ N

(D) p(k + 1) is true whenever p(k) is true where k ∈ N

Answer 1

Correct option (D)

Explanation:

P(n) ; n2 > 100

Let P(k) is true then k2 > 100

k2 + 2k + 1 > 100 + 2k + 1

(k + 1)2 > 100 + 2k + 1 (k + 1)2 > 100

∴ P(k + 1) is true