A) \[e+4\]
B) \[2+e\]
C) \[3+e\]
D) \[e\]
Correct Answer: B
Solution :
\[S=\frac{1}{1\ !}+\frac{4}{2\ !}+\frac{7}{3\ !}+\frac{10}{4\ !}+......+\frac{3n-2}{n\ !}+.......\infty \] Here \[{{T}_{n}}=\frac{3}{(n-1)\ !}-\frac{2}{n\ !}\] \[\Rightarrow S=\sum\limits_{n=1}^{\infty }{{{T}_{n}}=3\sum\limits_{n=1}^{\infty }{\frac{1}{(n-1)\ !}-2\sum\limits_{n=1}^{\infty }{\frac{1}{n\ !}}}}\] \[=3e-2(e-1)=e+2\].
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