JEE Mains · Maths · STD 11 - 12. limits
\(\operatorname{Lim}_{n \rightarrow \infty}\left\{\left(2^{\frac{1}{2}}-2^{\frac{1}{3}}\right)\left(2^{\frac{1}{2}}-2^{\frac{1}{5}}\right) \ldots \ldots\left(2^{\frac{1}{2}}-2^{\frac{1}{2 n+1}}\right)\right\}\) is equal to
- A \(\frac{1}{\sqrt{2}}\)
- B \(1\)
- C \(\sqrt{2}\)
- D \(0\)
Answer & Solution
Correct Answer
(D) \(0\)
Step-by-step Solution
Detailed explanation
\(\left(2^{\frac{1}{2}}-2^{\frac{1}{3}}\right)^n < \left(2^{\frac{1}{2}}-2^{\frac{1}{3}}\right)\left(2^{\frac{1}{2}}-2^{\frac{1}{5}}\right)\left(2^{\frac{1}{2}}-2^{\frac{1}{7}}\right)\)…
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