A) \[{{\log }_{e}}\frac{3}{2}\]
B) \[{{\log }_{10}}\frac{1}{2}\]
C) \[{{\log }_{e}}n\,!\]
D) \[{{\log }_{e}}\frac{1}{2}\]
Correct Answer: A
Solution :
Obviously \[0.5-\frac{{{(0.5)}^{2}}}{2}+\frac{{{(0.5)}^{3}}}{3}-....={{\log }_{e}}(1+0.5)\]\[={{\log }_{e}}\left( \frac{3}{2} \right)\].
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