Home
Class 11
MATHS
"If "x=1+a+a^(2)+...oo,|a|lt1,y=1+b+b^(2...

`"If "x=1+a+a^(2)+...oo,|a|lt1,y=1+b+b^(2)+...oo,|b|lt1,"then prove that ":(xy)/(x+y-1)=1+ab+a^(2)b^(2)+...oo`

A

`(xy)/(x+y-1)`

B

`(xy)/(x+y+1)`

C

`(xy)/(x-y-1)`

D

`(xy)/(x-y+1)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Similar Questions

Explore conceptually related problems

"If "y=x+x^(2)+x^(3)+...oo and |x|lt1, "then prove that "x=(y)/(1+y).

x=1+a+a^(2)+.........oo(|a|<1) and y=1+b+b^(2)+......oo(|b|<1 then find the value of 1+ab+a^(2)b^(2)+......oo

If =1+a+a^(2)+oo, where |a|< 1andy =1+b+b^(2)+oo, where |b|<1 prove that: 1+ab+a^(2)b^(2)+oo=(xy)/(x+y-1)

Let x=1+a+a^(2)+... and y=1+b+b^(2)+..., where |a|<1 and . Prove that 1+ab+a^(2)b^(2)+...=(xy)/(x+y-1)

If y =x+(1)/(x +(1)/(x+.....oo)) then prove that xdy/dx =y/(2y -x).

y =x^2+(1)/(x^2 +(1)/(x^2+.....oo)) then prove that xdy/dx =(2xy^2)/(1+y^2).

"If "x=a+(a)/(r)+(a)/(r^(2))+...oo,y=b-(b)/(r)+(b)/(r^(2))-...oo,"and "z=c+(c)/(r^(2))+(c)/(r^(4))+...oo," then prove that "(xy)/(z)=(ab)/(c).

If b=a+a^(2)+a^(3)+dot oo prove that a=(b)/(1+b)