Sequence And Series Question 616
Question: The value of $ {4^{1/3}}{{.4}^{1/9}}{{.4}^{1/27}}………..\infty $ is
[RPET 2003]
Options:
A) 2
B) 3
C) 4
D) 9
Show Answer
Answer:
Correct Answer: A
Solution:
$ {4^{1/3}}{{.4}^{1/9}}{{.4}^{1/27}}……\infty $
$ \therefore $ $ S={4^{1/3+1/9+1/27}}……\infty $
$ \Rightarrow $ $ S={4^{( \frac{1/3}{1-1/3} )}}={4^{\frac{1/3}{2/3}}} $
$ \Rightarrow $ $ S={4^{1/2}} $
$ \Rightarrow $ $ S=2 $ .
BETA
