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8. sequence and series — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS8. sequence and series1 Mark
MCQ
if $x = \,\frac{4}{3}\, - \,\frac{{4x}}{9}\, + \,\,\frac{{4{x^2}}}{{27}}\, - \,\,.....\,\infty $ , then $x$ is equal to
  • ✓
    only $1$
  • B
    $1$ or $-4$
  • C
    only $-4$
  • D
    $-1$ or $4$ 
✓

Answer

Correct option: A.
only $1$
a
$\Rightarrow x=\frac{4}{3}\left(\frac{1}{1+\frac{x}{3}}\right)=\frac{4}{3+x}$

$\Rightarrow 3 x+x^{2}=4$

$\Rightarrow x^{2}+3 x-4 \Rightarrow(x+4)(x-1)=0$

$\Rightarrow x=1,-4$

$\Rightarrow x=1$ only as $\left|-\frac{4}{3}\right|>1$

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