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"If "x=a+(a)/(r)+(a)/(r^(2))+...oo,y=b-(...

`"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).`

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To prove that \(\frac{xy}{z} = \frac{ab}{c}\), we will first find the values of \(x\), \(y\), and \(z\) using the formulas for the sums of infinite geometric series. ### Step 1: Calculate \(x\) The expression for \(x\) is given as: \[ x = a + \frac{a}{r} + \frac{a}{r^2} + \ldots \] ...
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