JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

1 of 1

Analyzing +4 | -1

The sum of the infinite series

\frac{{{2^2}}}{{2!}} + \frac{{{2^4}}}{{4!}} + \frac{{{2^6}}}{{6!}} + \ldots

is equal to

View answer and explanation

Correct option: C

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

Option C (

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

) is correct because it is derived from the power series expansion of

e^x

and

e^{-x}

, and then subtracting 1 to match the given series.

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