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8. Sequences and Series
medium
यदि $y = x - {x^2} + {x^3} - {x^4} + ......\infty $, तो $x$ का मान होगा
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 $
तब $xy = {x^2} – {x^3} + {x^4} – ……\infty $
जोड़ने पर, $y + xy = x + 0 + 0…… + 0$
$ \Rightarrow $ $x – xy = y$
$\Rightarrow x(1 – y) = y$
$\Rightarrow x = \frac{y}{{1 – y}}$.
वैकल्पिक : $y = \frac{x}{{1 – ( – x)}}$
$\Rightarrow y = \frac{x}{{1 + x}}$
$ \Rightarrow $ $y + yx = x $
$\Rightarrow x = \frac{y}{{1 – y}}$.
Standard 11
Mathematics
