Sequence And Series Question 115
Question: The value of $ \frac{2\frac{1}{2}}{1,!}+\frac{3\frac{1}{2}}{2,!}+\frac{4\frac{1}{2}}{3,!}+\frac{5\frac{1}{2}}{4,!}+……\infty $ is
Options:
A) $ 1+e $
B) $ \frac{1+e}{e} $
C) $ \frac{e-1}{e} $
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
The series is $ \frac{( 2+\frac{1}{2} )}{1!}+\frac{( 3+\frac{1}{2} )}{2!}+……\infty $ $ ={ \frac{2}{1!}+\frac{3}{2!}+….+\frac{n+1}{n!}+….\infty }+ $ $ \frac{1}{2}{ \frac{1}{1!}+\frac{1}{2!}+….\frac{1}{n!}+…\infty } $ $ =e+(e-1)+\frac{1}{2}(e-1)=\frac{5e}{2}-\frac{3}{2} $ .
BETA
