If $ S=\sum_\limits {n=0}^{\infty} \frac{(\log x)^{2 n}}{(2 n) !} $, then $ S= $

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

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Understanding +4 | -1

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

, then

S=

View answer and explanation

Correct option: C

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

Option C (

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

) is correct because the given series is the expansion of cosh(log x), which simplifies to the given expression.

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