If r > 1 and x = a + r a + r 2 a + … ∞ , y = b − r b + r 2 b − … ∞ and z = c + r 2 c + r 4 c + … ∞ , then z x y =

x = 1 − r 1 a = r − 1 a r , y = 1 + r 1 b = r + 1 b r , z = 1 − r 2 1 c = r 2 − 1 c r 2 . z x y = r − 1 a r ⋅ r + 1 b r ⋅ c r 2 r 2 − 1 = c ab .

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Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesG.P.Medium2 minQB

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If $r > 1$ and $x = a + \frac{a}{r} + \frac{a}{r ^{2}} + \dots \infty, y = b - \frac{b}{r} + \frac{b}{r ^{2}} - \dots \infty$ and $z = c + \frac{c}{r ^{2}} + \frac{c}{r ^{4}} + \dots \infty$ , then $\frac{x y}{z} =$

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Answer:

Solution:

$x = \frac{a}{1 - \frac{1}{r}} = \frac{a r}{r - 1}, y = \frac{b}{1 + \frac{1}{r}} = \frac{b r}{r + 1}, z = \frac{c}{1 - \frac{1}{r ^{2}}} = \frac{c r ^{2}}{r ^{2} - 1}$ . $\frac{x y}{z} = \frac{a r}{r - 1} \cdot \frac{b r}{r + 1} \cdot \frac{r ^{2} - 1}{c r ^{2}} = \frac{ab}{c}$ .

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:G.P.

⏱ 2mℹ️ Source: QB

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