A) \[2\,e\]
B) \[3\,e\]
C) \[3\,e-1\]
D) \[e\]
Correct Answer: B
Solution :
\[\frac{1.2}{1\ !}+\frac{2.3}{2\ !}+\frac{3.4}{3\ !}+\frac{4.5}{4\ !}+.........\infty \], Here \[{{T}_{n}}=\frac{n(n+1)}{n\ !}=\frac{n+1}{(n-1)\ !}=\frac{(n-1)+2}{(n-1)\ !}\] \[=\frac{1}{(n-2)\ !}+\frac{2}{(n-1)\ !}\] \[\Rightarrow S=\Sigma {{T}_{n}}=e+2e=3e\].
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