A) \[\log \,(2/e)\]
B) \[\log \,(e/2)\]
C) 2/e
D) e/2
Correct Answer: B
Solution :
\[\frac{1}{2.3}+\frac{1}{4.5}+\frac{1}{6.7}+.....\] \[=\left( \frac{1}{2}-\frac{1}{3} \right)+\left( \frac{1}{4}-\frac{1}{5} \right)+\left( \frac{1}{6}-\frac{1}{7} \right)+......\infty =1-{{\log }_{e}}2\] \[={{\log }_{e}}e-{{\log }_{e}}2=\log \left( \frac{e}{2} \right)\].
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