[JEE Main 2008] statement 1 for every natural n 2 1 sqrt 1 1 sqrt 2 1
Statement-1: For every natural $n\ge2$, $\frac1{\sqrt1}+\frac1{\sqrt2}+\cdots+\frac1{\sqrt n}>\sqrt n$. Statement-2: For every natural $n\ge2$, $\sqrt{n(n+1)}<n+1$.
(a) S-1 false, S-2 true
(b) S-1 true, S-2 true; S-2 correctly explains S-1
(c) S-1 true, S-2 true; S-2 not a correct explanation
(d) S-1 true, S-2 false
1 Answer
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✓ Accepted
· 2d ago
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Correct answer: (c) S-1 true, S-2 true; S-2 not a correct explanation
Both statements are true. The induction step for S-1 uses $\sqrt{n(n+1)}>n$, not the bound in S-2, so S-2 does not explain S-1.
JEE Main 2008 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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