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 = `

Explanation

We have,
`x=a/(1-1/r)=ar/(r-1)`
`y=b/(1-(-1/r))=(br)/(1+r)`
`z=c/(1-1/r^(2))`
`thereforexy=((ar)/(r-1))((br)/(r+1))=(abr^(2))/(r^(2)-1)`
`therefore (xy)/z=[((abr^(2))/(r^(2)-1))/((cr^(2))/(r^(2)-1))]=(ab)/c`