If `y=x+x^(2)+x^(3)+....` up to infinite terms where `xlt1`, then which one of the following is correct?

Options

A. `x=(y)/(1+y)`
B. `x=(y)/(1-y)`
C. `x=(1+y)/(y)`
D. `x=(1-y)/(y)`

Answer

A

Explanation

`y=x+x^(2)+x^(3)+...."upto infinite terms."`
`x+x^(2)+x^(3)+......" is a G.P. with a = x and r = x."`
`:.y=(x)/(1-x)`
`impliesy-xy=x`
`impliesx+xy=x`
`impliesx(1+y)=y`
`impliesx=(y)/(1+y).`