JEE MATHEMATICS MCQ: LIMITS

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Application +4 | -1

\lim _{n \rightarrow \infty}\left\{\frac{1+\frac{1}{3}+\frac{1}{9}+\cdots \text { to }(n+1) \text { terms }}{1+\frac{1}{2}+\frac{1}{4}+\cdots \text { to }(n+1) \text { terms }}\right\}=

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Correct option: D

\frac{2}{3}

Option A (2/3) is correct because the limit simplifies to 2/3 after evaluating the geometric series and taking the limit as n approaches infinity.

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