Sequence And Series Question 618
Question: If $ y=x+x^{2}+x^{3}+…….,\infty ,,thenx= $
[DCE 1999]
Options:
A) $ \frac{y}{1+y} $
B) $ \frac{1-y}{y} $
C) $ \frac{y}{1-y} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ y=\frac{x}{1-x} $ (Infinite G.P.)
$ \therefore y-yx=x $ or $ y=x,(1+y) $ i.e., $ x=\frac{y}{1+y} $ .