A) \[\frac{1}{2}\left( 1-2x+\frac{5}{2}{{x}^{2}}-.... \right)\]
B) \[\frac{1}{16}\left( 1-2x+\frac{5}{2}{{x}^{2}}-.... \right)\]
C) \[\frac{1}{16}\left( 1+2x+\frac{5}{2}{{x}^{2}}+.... \right)\]
D) \[\frac{1}{2}\left( 1+2x+\frac{5}{2}{{x}^{2}}+.... \right)\]
Correct Answer: B
Solution :
\[{{(x+2)}^{-4}}={{2}^{-4}}{{\left[ 1+\frac{x}{2} \right]}^{-4}}=\frac{1}{16}\left[ 1-2x+\frac{5}{2}{{x}^{2}}-.... \right]\]
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