If y = x + x^2 + x^3 + ....... , , , then , ,x = - Vidyadip

MCQ

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

✓
$\frac{y}{{1 + y}}$
B
$\frac{{1 - y}}{y}$
C
$\frac{y}{{1 - y}}$
D
None of these

✓

Answer

Correct option: A.

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

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

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

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

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