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8. Sequences and Series
easy
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