Question

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please solve this 80th question

Answer 1

$y = x - {x}^{2} + {x}^{3} - {x}^{4} - - upto\:infinity \\ y = (x + {x}^{3} + {x}^{5} - - - ) - ( {x}^{2} \\ + {x}^{4} - - - - ) \\ it \: an \: gp \\ applying \: sum \: of \: infinite \: gp =\frac{a}{1-r}\\ where\: a\: is\: first\: term\\ and\: r\: is\: the\: common\: ratio \\ y = \frac{x}{1 - {x}^{2} } - \frac{ {x}^{2} }{1 - {x}^{2} } \\ y = \frac{x - {x}^{2} }{1 - {x}^{2} } \\ y = \frac{x(1 - x)}{(1 - x)(1 + x)} \\ y = \frac{x}{1 + x} \\ y + yx = x \\ y = x(1 - y) \\ x = \frac{y}{1 - y}$

Answer 2

Correct answer to this question is option (A) .
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