A) \[{{\log }_{e}}(a-b)\]
B) \[{{\log }_{e}}\left( \frac{a}{b} \right)\]
C) \[{{\log }_{e}}\left( \frac{b}{a} \right)\]
D) \[{{e}^{\left( \frac{a-b}{a} \right)}}\]
Correct Answer: B
Solution :
\[\left( \frac{a-b}{a} \right)+\frac{1}{2}{{\left( \frac{a-b}{a} \right)}^{2}}+\frac{1}{3}{{\left( \frac{a-b}{a} \right)}^{3}}+......\] \[=-{{\log }_{e}}\left( 1-\frac{a-b}{a} \right)=-{{\log }_{e}}\left( \frac{b}{a} \right)={{\log }_{e}}\left( \frac{a}{b} \right)\].
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