If $S = \mathop \sum \limits_{n = 2}^\infty {\;^n}{C_2}\frac{{{3^{n - 2}}}}{{n\;!}},$ then $S$ equals

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Application +4 | -1

S = \sum \limits_{n = 2}^\infty {\;^n}{C_2}\frac{{{3^{n - 2}}}}{{n\;!}},

then

S

equals

View answer and explanation

Correct option: B

\frac{1}{2}{e^3}

Option B (

\frac{1}{2}{e^3}

) is correct because the series can be simplified and recognized as a Taylor series expansion of the exponential function.

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