Sequence And Series Question 567
Question: $ \frac{1,.,2}{1,!}+\frac{2,.,3}{2,!}+\frac{3,.,4}{3,!}+\frac{4,.,5}{4,!}+…..\infty = $
Options:
A) $ 2,e $
B) $ 3,e $
C) $ 3,e-1 $
D) $ e $
Show Answer
Answer:
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 $ .
BETA
