Sequence And Series Question 230
Question: The value of $ \sqrt{e} $ will be
[UPSEAT 1999]
Options:
A) 1.648
B) 1.547
C) 1.447
D) 1.348
Show Answer
Answer:
Correct Answer: A
Solution:
$ \because e^{x}=1+x+\frac{x^{2}}{2!}+\frac{x^{3}}{3!}+…. $ Putting $ x=\frac{1}{2} $ on both the sides $ \sqrt{e}={e^{1/2}} $ = $ 1+\frac{1}{2}+\frac{{{( \frac{1}{2} )}^{2}}}{2!}+\frac{{{( \frac{1}{2} )}^{3}}}{3!}+\frac{{{( \frac{1}{2} )}^{4}}}{4!}+…. $ = $ 1+\frac{1}{2}+\frac{1}{2^{2}2}+\frac{1}{2^{3}6}+\frac{1}{2^{4}.24}+…. $ $ 1+0.5+0.1250+0.0208+0.0026 $ $ =1.648 $ , (approximately).
BETA
