1+a+a^(2)+......oo,y=1+b+b^(2)+......oo" if "1+ab+a^(2)b^(2)+............" to "oo=S" then "S=

If x=1+a+a^(2)+...oo, a lt 1 and y=1+b+b^(2)+...oo, b lt 1, then 1+ab+a^(2)b^(2)+...oo :

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

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 A=1+r^a+r^(2a)+ ......... to oo and B=1+r^b+r^(2b)+........... to oo , prove that r=((A-1)/A)^(1//a)=((B-1)/B)^(1//b) .

If x=1+a+a^(2)+…….oo,y=1+b+b^(2)…….oo then 1+ab+a^(2)b^(2)+……….oo,|a|lt1,|b|lt1 is

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=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 "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 "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