Question

If $y=x-x^2+x^3-x^4+$..... then $x$ is equal to

• A. $\frac{1-y}{y}$
• B. $\frac{y}{1-y}$
• C. $\frac{1+y}{y}$
• D. $\frac{y}{1+y}$

Answer 1

Answer: (B)

$\frac{y}{1-y}$

• The R.H.S. of the equation is a sequence in geometric progressionwith infinite terms, with,
• first term, i.e.,a = x, and
• common ratio, i.e.,r = -x
• Now, sum of a sequence in geometric progression with infinite terms is given by
  

S = a/(1-r)

• Here,x∈(-1, 1], otherwise the sum of the terms will be infinite.
  

Therefore,

• R.H.S. =x/(1+x)
  

Now, y = x/(1+x)

• ⇒ y+xy = x
  
• ⇒ y = x(1-y)
  
• ⇒x = y/(1-y) = answer