$\mathop \sum \limits_{n = 0}^\infty \frac{{{{\left( {{{\log }_e}x} \right)}^n}}}{{n\;!}}\;{\rm{is\;equal\;to}}$

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

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Understanding +4 | -1

\sum \limits_{n = 0}^\infty \frac{{{{\left( {{{\log }_e}x} \right)}^n}}}{{n\;!}}\;\mathrm{is\;equal\;to}

View answer and explanation

Correct option: B

x

Option B (

x

) is correct because the given series is the Taylor series expansion of

e^y

where

y = \log_e x

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