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} $ .