Sequence And Series Question 4
Question: $ 3+\frac{5}{1,!}+\frac{7}{2,!}+\frac{9}{3,!}+…..\infty = $
Options:
A) $ 3,e $
B) $ 5,e $
C) $ 5,e-1 $
D) None of these
Show Answer
Answer:
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 $ .
BETA
