Sequence And Series Question 536
Question: $ \frac{1}{1,!}+\frac{4}{2,!}+\frac{7}{3,!}+\frac{10}{4,!}+…..\infty = $
Options:
A) $ e+4 $
B) $ 2+e $
C) $ 3+e $
D) $ e $
Show Answer
Answer:
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 $ .
BETA
