A) \[\frac{{{e}^{4}}+{{e}^{-4}}}{4}\]
B) \[\frac{{{e}^{4}}-{{e}^{-4}}}{4}\]
C) \[\frac{{{e}^{4}}+{{e}^{-4}}}{8}\]
D) \[\frac{{{e}^{4}}-{{e}^{-4}}}{8}\]
Correct Answer: D
Solution :
\[S=1+\frac{{{4}^{2}}}{3\ !}+\frac{{{4}^{4}}}{5\ !}+........\infty \] \[=\frac{1}{4}\left\{ 4+\frac{{{4}^{3}}}{3\ !}+\frac{{{4}^{5}}}{5\,!}+...... \right\}=\frac{1}{4}\left( \frac{{{e}^{4}}-{{e}^{-4}}}{2} \right)\].
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