A) \[1-2x+3{{x}^{2}}-....\]
B) \[1+2x+3{{x}^{2}}+\]....
C) \[1-\frac{2}{x}+\frac{3}{{{x}^{2}}}-....\]
D) \[\frac{1}{{{x}^{2}}}-\frac{2}{{{x}^{3}}}+\frac{3}{{{x}^{4}}}-\]...
Correct Answer: D
Solution :
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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