If `x=a+a/r+a/(r^2)+oo,y=b-b/r+b/(r^2)+oo,a n dz=c+c/(r^2)+c/(r^4)+oo,` prove that `(x y)/z=(a b)/c`

Explanation

To prove that \(\frac{xy}{z} = \frac{ab}{c}\), we start by evaluating \(x\), \(y\), and \(z\) based on the given infinite series.

### Step 1: Calculate \(x\)
The expression for \(x\) is given as:
\[ x = a + \frac{a}{r} + \frac{a}{r^2} + \ldots \]
This is a geometric series where the first term \(a_1 = a\) and the common ratio \(r_1 = \frac{1}{r}\).
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