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The sum of the series \( \sum_{n=1}^{\infty} \frac{n^{2}+6 n+10}{(2 n+1) !} \) is equal to : [JEE Main 2021, 26 Feb (Shi…

Q1

The sum of the series \( \sum_{n=1}^{\infty} \frac{n^{2}+6 n+10}{(2 n+1) !} \) is equal to :

[JEE Main 2021, 26 Feb (Shift 2)]

a

\( \frac{41}{8} e+\frac{19}{8} e^{-1}-10 \)

b

\( \frac{41}{8} e-\frac{19}{8} e^{-1}-10 \)

c

\( \frac{41}{8} e+\frac{19}{8} e^{-1}+10 \)

d

\( -\frac{41}{8} e+\frac{19}{8} e^{-1}-10 \)

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