`y=b-b/r+b/(r^2)-....oo`

If |r| gt 1, x = a + a/r + a/r^(2) + .......... infty , y = b - b/r + b/r^(2) - ......... infty and z = c + c/r^(2) + c/r^(4) + ...... infty , then the value of (xy)/z =

if r>1 and x=a+(a)/(r)+(a)/(r^(2))+.........oo,y=b-(b)/(r)+(b)/(r^(2))-(b)/(r^(2)) and z=c+(c)/(r^(2))+(c)/(r^(4))+............oo then (xy)/(z)

If r>1 and x=a+(a)/(r)+(a)/(r^(2))............,y=b+(b)/(r)+(b)/(r^(2))...... and z=b+(b)/(r)+(b)/(r^(2))+.......... Then value of (xy)/(z^(2)) is

If A=1+r^a+r^(2a)+...oo=a and B=1+r^b+r^(2b)+...oo=b then a/b is equal to

If A=1+r^(2)+r^(2a)+...oo=a and B=1+r^(b)+r^(2b)+...oo=b then (a)/(b) is equal to

If, for real numbers a, b, c, r with |r| gt 1, x = a + (a)/(r ) + (a)/(r^(2)) +…, " " y = b - (b)/(r ) + (b)/(r^(2)) - (b)/(r^(3))+… and z = c + (c )/(r^(2)) + (c )/(r^(4)) +… , then show that xyc = abz.

"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

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 A=1+r^(a)+r^(2 a)+r^(3 a)+.. . to oo and lebrge B=1+r^(b)+r^(2 b)+......infty then (a)/(b) is equal to

Sum to infinity 1+(1+b) r+(1+b+b^(2))r^(2) +(1+b+b^(2)+b^(3))r^(3)+.... ,r and b being proper fractions.