JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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S = \sum \limits_{n = 0}^\infty \frac{{{{\left( {\log x} \right)}^{2n}}}}{{\left( {2\;n} \right)\;!}},

then

S

equals

View answer and explanation

Correct option: C

\frac{1}{2}\left( {x + {x^{ - 1}}} \right)

Option C is correct because the given series is the Taylor series expansion of cosh(log x), which simplifies to (x + x^(-1))/2.

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