A) \[\frac{1}{2}\]
B) \[-1\]
C) 1
D) none of these
Correct Answer: A
Solution :
\[2{{\log }_{e}}x-{{\log }_{e}}(x+1)-{{\log }_{e}}(x-1)\] \[=\log {{x}^{2}}-\log ({{x}^{2}}-1)\] \[=-\log \left( \frac{{{x}^{2}}-1}{{{x}^{2}}} \right)=-\log \left( 1-\frac{1}{{{x}^{2}}} \right)\] \[=\left[ \frac{1}{{{x}^{2}}}+\frac{1}{2}{{\left( \frac{1}{{{x}^{2}}} \right)}^{2}}+\frac{1}{3}{{\left( \frac{1}{{{x}^{2}}} \right)}^{3}}+... \right]\] The coefficient of \[{{x}^{-4}}=\frac{1}{2}\]
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