A) \[3\,e\]
B) \[5\,e\]
C) \[5\,e-1\]
D) None of these
Correct Answer: B
Solution :
\[3+\frac{5}{1\ !}+\frac{7}{2\ !}+\frac{9}{3\ !}+......\infty \] \[{{T}_{n}}=\frac{2n+1}{(n-1)\ !}=\frac{2(n-1)}{(n-1)\ !}+\frac{3}{(n-1)\ !}\]\[=\frac{2}{(n-2)\ !}+\frac{3}{(n-1)\ !}\] Now, sum \[{{S}_{n}}=2\sum\limits_{n=1}^{\infty }{\frac{1}{(n-2)\ !}+3\sum\limits_{n=1}^{\infty }{\frac{1}{(n-1)\ !}}}\] \[=2e+3e=5e\].
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