A) \[1+e\]
B) \[\frac{1+e}{e}\]
C) \[\frac{e-1}{e}\]
D) None of these
Correct Answer: D
Solution :
The series is \[\frac{\left( 2+\frac{1}{2} \right)}{1!}+\frac{\left( 3+\frac{1}{2} \right)}{2!}+......\infty \] \[=\left\{ \frac{2}{1!}+\frac{3}{2!}+....+\frac{n+1}{n!}+....\infty \right\}+\]\[\frac{1}{2}\left\{ \frac{1}{1!}+\frac{1}{2!}+....\frac{1}{n!}+...\infty \right\}\] \[=e+(e-1)+\frac{1}{2}(e-1)=\frac{5e}{2}-\frac{3}{2}\].
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