Question

Statement I For every natural number n ≥ 2.

1/√1 + 1/√2 + .... + 1/√n > √n

Statement II For every natural number n ≥ 2, √(n(n + 1)) < n + 1.

(a) Statement I is false, Statement II is true 

(b) Statement I is true, Statement II is true; Statement II is a correct explanation of Statement I

(c) Statement I is true, Statement II is true; Statement II is not a correct explanation of Statement I

(d) Statement I is true, Statement II is false

Answer 1

Correct option (c) Statement I is true, Statement II is true; Statement II is not a correct explanation of Statement I

Explanation:

By mathematical induction, statement I is true for all n ≥ 2.

By mathematical induction. Statement ll is true but Statement ll rs not a correct explanation of Statement l.