If \( S \) denotes the sum of an infinite G.P. and \( S_{1} \) denotes the sum of the squares of...

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If \( S \) denotes the sum of an infinite G.P. and \( S_{1} \) denotes the sum of the squares of its terms, then prove that the first term and common ratio are respectively \( \frac{2 S S_{1}}{S^{2}+S_{1}} \) and \( \frac{S^{2}-S_{1}}{S^{2}+S_{1}} \).
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