If - r gt-1- and - x-a-a-r-a-r-2- nbsp-y-b-b-r-b-r-2- nbsp-and - z-c-c-r-c-r-2- nbsp-then value of - xy-z-2- is- ab-c-2- ab-c-2r- abr-c-none of these

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Sum of Infinite Terms of a GP

If r g...

Question

If $r > 1$ and $x = a + a / r + a / r^{2} + . . ., y = b + b / r + b / r^{2} + . . .$ and $z = c + c / r + c / r^{2} + . . .,$ then value of $x y / z^{2}$ is

a b / c^{2}

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a b r / c

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a b / c^{2} r

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none of these

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r > 1

x = a + \frac{a}{r} + \frac{a}{r^{2}} +

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\frac{x y}{z} =

r > 1

x = a + \frac{a}{r} + \frac{a}{r^{2}} + . . . . . .

\infty,

y = b - \frac{b}{r} + \frac{b}{r^{2}} - . . .

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z = c + \frac{c}{r^{2}} + \frac{c}{r^{4}} + . . . .

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\frac{x y}{z} =

x = a + \frac{a}{r} + \frac{a}{r^{2}} + \dots \infty,

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| r | > 1,

\frac{x y}{z}

\frac{p}{a} + \frac{q}{b} + \frac{r}{c} = 1

\frac{a}{p} + \frac{b}{q} + \frac{c}{r} = 0

\frac{p^{2}}{a^{2}} + \frac{q^{2}}{b^{2}} + \frac{r^{2}}{c^{2}}

If $r > 1$ and
$x = a + \frac{a}{r} + \frac{a}{r^{2}}$
$y = b + \frac{b}{r} + \frac{b}{r^{2}}$
$z = c + \frac{c}{r} + \frac{c}{r^{2}},$

then the value of $\frac{x y}{z^{2}}$ is ___.

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