A) ½
B) 1/3
C) ¼
D) None of these
Correct Answer: A
Solution :
\[\underset{n\to \infty }{\mathop{\lim }}\,\frac{1}{2}\left[ \left( 1-\frac{1}{3} \right)+\left( \frac{1}{3}-\frac{1}{5} \right)+\left( \frac{1}{5}-\frac{1}{7} \right)+.... \right.\] \[\left. +\left( \frac{1}{(2n-1)}-\frac{1}{(2n+1)} \right) \right]\] \[=\underset{n\to \infty }{\mathop{\lim }}\,\frac{1}{2}\left[ 1-\frac{1}{2n+1} \right]=\frac{1}{2}\].
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