A) \[log\text{ }2\]
B) \[log\text{ }3\]
C) \[2\text{ }log\text{ }2-1\]
D) \[2\text{ }log\text{ }3-1\]
Correct Answer: C
Solution :
Given, \[\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{3.4}-\frac{1}{4.5}+....\] \[=\left( 1-\frac{1}{2} \right)-\left( \frac{1}{2}-\frac{1}{3} \right)+\left( \frac{1}{3}-\frac{1}{4} \right)...\] \[=1-2.\frac{1}{2}+2.\frac{1}{3}-2.\frac{1}{4}+....-1+1\] \[=2\left[ 1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+..... \right]-1\] \[=2\text{ }log(1+1)-1\] \[=2\text{ }log\text{ }2-1\]
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