Sequence And Series Question 626
Question: If the sum of the series $ 1+\frac{2}{x}+\frac{4}{x^{2}}+\frac{8}{x^{3}}+….\infty $ is a finite number, then
[UPSEAT 2002]
Options:
A) $ x>2 $
B) $ x>-2 $
C) $ x>\frac{1}{2} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Common ratio $ (r)=\frac{2}{x} $ For sum to be finite $ r<1 $
$ \Rightarrow $ $ \frac{2}{x}<1 $
$ \Rightarrow $ $ 2<x $
$ \Rightarrow $ $ x>2 $ .
BETA
