If y = x - {x^2} + {x^3} - {x^4} + ......inft | vedclass

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Question

(d) $y = x - {x^2} + {x^3} - {x^4} + ........\infty $

then $xy = {x^2} - {x^3} + {x^4} - ......\infty $

Adding, $y + xy = x + 0 + 0...... + 0$

Vedclass · Accepted Answer

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

Vedclass · Answer

(d) $y = x - {x^2} + {x^3} - {x^4} + ........\infty $

then $xy = {x^2} - {x^3} + {x^4} - ......\infty $

Adding, $y + xy = x + 0 + 0...... + 0$

$ \Rightarrow $$x - xy = y $

$\Rightarrow x(1 - y) = y$

$\Rightarrow x = \frac{y}{{1 - y}}$.

Aliter : $y = \frac{x}{{1 - ( - x)}} $

$\Rightarrow y = \frac{x}{{1 + x}}$

$ \Rightarrow $$y + yx = x$

$\Rightarrow x = \frac{y}{{1 - y}}$.

If $y = x - {x^2} + {x^3} - {x^4} + ......\infty $, then value of $x$ will be

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