If y = x + {x^2} + {x^3} + .......,∞ ,,{rm{then}},,x =

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8. Sequences and Series

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If $y = x + {x^2} + {x^3} + .......\,\infty ,\,{\rm{then}}\,\,x = $

A

$\frac{y}{{1 + y}}$

B

$\frac{{1 - y}}{y}$

C

$\frac{y}{{1 - y}}$

D

None of these

Solution

(a) $y = \frac{x}{{1 – x}}$(Infinite $G.P.$)

$\therefore y – yx = x$ or $y = x\,(1 + y)$

$i.e.$, $x = \frac{y}{{1 + y}}$.

Standard 11

Mathematics

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