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binomial theoram — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSbinomial theoram1 Mark
MCQ
If $|x| > 1$, then ${(1 + x)^{ - 2}}$ =
  • A
    $1 - 2x + 3{x^2} - ....$
  • B
    $1 + 2x + 3{x^2} + $....
  • C
    $1 - \frac{2}{x} + \frac{3}{{{x^2}}} - ....$
  • ✓
    $\frac{1}{{{x^2}}} - \frac{2}{{{x^3}}} + \frac{3}{{{x^4}}} - $...
✓

Answer

Correct option: D.
$\frac{1}{{{x^2}}} - \frac{2}{{{x^3}}} + \frac{3}{{{x^4}}} - $...
d
(d) Given that $|x|>1.$

So given expression can be written as
${x^{ - 2}}{\left( {1 + \frac{1}{x}} \right)^{ - 2}} = {x^{ - 2}}\left[ {1 - \frac{2}{x} + \frac{3}{{{x^2}}} - \frac{4}{{{x^3}}} + ....} \right]$

$ = \left[ {\frac{1}{{{x^2}}} - \frac{2}{{{x^3}}} + \frac{3}{{{x^4}}} - \frac{4}{{{x^5}}} + ....} \right]$

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