Sequence And Series Question 266
Question: Sum of the infinite series $ 1+2+\frac{1}{2!}+\frac{2}{3!}+\frac{1}{4!}+\frac{2}{5!}+….. $ is
[Roorkee 2000]
Options:
A) $ e^{2} $
B) $ e+{e^{-1}} $
C) $ \frac{e-{e^{-1}}}{2} $
D) $ \frac{3e-{e^{-1}}}{2} $
Show Answer
Answer:
Correct Answer: D
Solution:
Sum of series $ =1+2+\frac{1}{2!}+\frac{2}{3!}+\frac{1}{4!}+\frac{2}{5!}+….. $ $ =( 1+\frac{1}{2!}+\frac{1}{4!}+…. )+2( 1+\frac{1}{3!}+\frac{1}{5!}+….. ) $ = $ \frac{e+{e^{-1}}}{2}+2.\frac{e-{e^{-1}}}{2}=\frac{3e-{e^{-1}}}{2} $ .
BETA
