JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Analyzing +4 | -1

\frac{1}{2} - \frac{1}{{{{2.2}^2}}} + \frac{1}{{{{3.2}^3}}} - \frac{1}{{{{4.2}^4}}} + \ldots

is equal to

View answer and explanation

Correct option: C

{\log _e}\left( {\frac{3}{2}} \right)

Option C (

{\log _e}(\frac{3}{2})

) is correct because the given series is a direct application of the Maclaurin series expansion of

\log_e(1+x)

with

x = \frac{1}{2}

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