JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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The value of

\frac{{\sqrt 2 - 1}}{{\sqrt 2 }} + \frac{{3 - 2\sqrt 2 }}{4} + \frac{{5\sqrt 2 - 7}}{{6\sqrt 2 }} + \frac{{17 - 12\sqrt 2 }}{{16}} + \ldots + \ldots + \mathrm{ad}.\mathrm{\;inf}.,

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Correct option: B

{\log _e}\sqrt 2

Option B is correct because the given series can be rewritten as a logarithmic series, and its sum converges to

{\log _e}\sqrt 2

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