Gujarati
8. Sequences and Series
medium

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

A

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

B

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

C

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

D

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

Solution

(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$

$\Rightarrow x = \frac{y}{{1 – y}}$.

Standard 11
Mathematics

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