Sequence And Series Question 545
Question: If $ y=x-x^{2}+x^{3}-x^{4}+……\infty $ , then value of x will be
[MNR 1975; RPET 1988; MP PET 2002]
Options:
A) $ y+\frac{1}{y} $
B) $ \frac{y}{1+y} $
C) $ y-\frac{1}{y} $
D) $ \frac{y}{1-y} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ y=x-x^{2}+x^{3}-x^{4}+……..\infty $ then $ xy=x^{2}-x^{3}+x^{4}-……\infty $ Adding, $ y+xy=x+0+0……+0 $
$ \Rightarrow $ $ x-xy=y\Rightarrow x(1-y)=y\Rightarrow x=\frac{y}{1-y} $ . Aliter: $ y=\frac{x}{1-(-x)}\Rightarrow y=\frac{x}{1+x} $
$ \Rightarrow $ $ y+yx=x\Rightarrow x=\frac{y}{1-y} $ .
BETA
