Sequence And Series Question 291
Question: The sum of the series $ \frac{1}{2,!}-\frac{1}{3,!}+\frac{1}{4,!}-….. $ is
[DCE 2002]
Options:
e
B) $ {e^{-,\frac{1}{2}}} $
C) $ {e^{-,2}} $
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
We know, $ e^{x}=1+x+\frac{x^{2}}{2!}+\frac{x^{3}}{3!}+\frac{x^{4}}{4!}+…. $ Put $ x=-1 $
$ \Rightarrow {e^{-1}}=1-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}-\frac{1}{5!}+….. $
Þ $ {e^{-1}}=\frac{1}{1!}-\frac{1}{2!}+\frac{1}{3!}-\frac{1}{4!}+….. $
BETA
