`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^2b^2+......oo`

If x = 1+a+a^2+..........oo where abs(a)lt1 and y=1+b+b^2+........oo where abs(b)lt1 .Prove that 1+ab+a^2b^2+.......oo = (xy)/(x+y-1)

If (x^(2)+x)/(1-x)=a_(1)x+a_(2)x^(2)+............oo,|X|< then

if x=1+y+y^(2)+............ to oo then y is equal to

if y=x^2+1/(x^2+1/(x^2+1/(x^2+...............oo))) then (dy)/(dx)

for 0

If |x|lt(1)/(2), what is the value of 1+[(x)/(1-x)]+[(n(n+1))/(2!)][(x)/(1-x)]^(2)+............+oo ?

If (e^(x) -1)^(2) =a_0 +a_(1)x +a_(2) x^2 + ......oo then a_4 =

If x = 1 + a + a^(2) +… oo (-1 lt a lt 1) and y = 1 + b + b^(2)+ … oo (-1 lt b lt 1) , prove that, 1+ab + a^(2)b^(2)+ … oo = (xy)/(x+y - 1)

Let a,b,c be in A.P. and |a|lt1,|b|lt1|c|lt1. if x=1+a+a^(2)+ . . . . oo , y=1+b+b^(2)+ . . . .oo , z=1+c+c^(2)+ . . . oo , then x,y,z are in