Statement - 1: For every natural number n ≥ 2 , 1 + 1/√(2) + + 1/√(n) > √(n) .Statement - 2: For every natural number n ≥ 2 , √(n(n+1)) < n + 1 . - Mathematics MCQ AIEEE 2026 | ExamTest.live

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Statement - 1: For every natural number n \geq 2, 1 + \frac{1}{2} + \dots + \frac{1}{n} > n .Statement - 2: For every natural number n \geq 2, n (n + 1) < n + 1 .

A $Statement - 1 is false, Statement - 2 is true$
B $Statement - 1 is true, Statement - 2 is true; Statement - 2 is a correct explanation for Statement - 1$
C $Statement - 1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1$
D $Statement - 1 is true, Statement - 2 is false$

Solution & Step-by-step Explanation

Statement 1: 1 + \frac{1}{2} + \dots + \frac{1}{n} > \frac{1}{n} + \frac{1}{n} + \dots + \frac{1}{n} (n times) ⟹ 1 + \frac{1}{2} + \dots + \frac{1}{n} > \frac{n}{n} = n .So, Statement 1 is true.Statement 2: n (n + 1) < (n + 1) (n + 1) = n + 1 for n \geq 2 .So, Statement 2 is true.However, Statement 2 is a trivial property of square roots and does not provide the logical basis for the summation inequality in Statement 1. Statement 1 is proved by comparing terms to the smallest term 1/ n .

Try it yourself before checking the explanation above.

Statement - 1: For every natural number n \geq 2, 1 + \frac{1}{2} + \dots + \frac{1}{n} > n .Statement - 2: For every natural number n \geq 2, n (n + 1) < n + 1 .

Statement - 1 is false, Statement - 2 is true

Statement - 1 is true, Statement - 2 is true; Statement - 2 is a correct explanation for Statement - 1

Statement - 1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1

Statement - 1 is true, Statement - 2 is false

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