If \( a_{1}, a_{2}, a_{3}, \ldots \) are in \( G P \) with first term \( a \) and common ratio \....

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If \( a_{1}, a_{2}, a_{3}, \ldots \) are in \( G P \) with first term \( a \) and common
P
ratio \( r \), then
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\( \frac{a_{1} a_{2}}{a_{1}^{2}-a_{2}^{2}}+\frac{a_{2} a_{3}}{a_{2}^{2}-a_{3}^{2}}+\frac{a_{3} a_{4}}{a_{3}^{2}-a_{4}^{2}}+\ldots .+\frac{a_{n-1} a_{n}}{a_{n-1}^{2}-a_{n}^{2}} \) is equal to
(1) \( \frac{n r}{1-r^{2}} \)
(2) \( \frac{(n-1) r}{1-r^{2}} \)
(3) \( \frac{n r}{1-r} \)
(4) \( \frac{(n-1) r}{1-r} \)


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