The ratio of the sum of the cubes of an infinitely decreasing GP to the sum of its squares is \(....

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The ratio of the sum of the cubes of an infinitely
\( \mathrm{P} \)
decreasing GP to the sum of its squares is \( 12: 13 \). The sum of the first and second terms is equal to \( 4 / 3 \). If \( a \), \( r \) and \( s_{\infty} \) denote the first term, common ratio and sum of infinity of the \( G P \), then
(1) \( r=1 / 3, a=6 / 5, s_{\infty}=9 / 5 \)
(2) \( r=1 / 3, a=1 \)
(3) \( r=-4 / 3, a=-1 / 3, s_{\infty}=-1 / 7 \)
(4) \( s_{\infty}=3 / 2 \)


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