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 :
Key Idea: In any series, if denominator is not in factorial terms, then the given series may be logarithmic series. Let \[S=\left( \frac{a-b}{a} \right)+\frac{1}{2}{{\left( \frac{a-b}{a} \right)}^{2}}+\frac{1}{3}{{\left( \frac{a-b}{a} \right)}^{3}}+...\] \[=-\log \left( 1-\left( \frac{a-b}{a} \right) \right)\] \[=-\log \left( \frac{b}{a} \right)\] \[=\log \frac{a}{b}\]
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