A) 0
B) \[-\frac{1}{2}\]
C) \[\log \left( \frac{2}{3} \right)\]
D) None of these
Correct Answer: B
Solution :
\[\underset{n\to \infty }{\mathop{\lim }}\,\,\left[ \frac{1}{1-{{n}^{2}}}+\frac{2}{1-{{n}^{2}}}+.....+\frac{n}{1-{{n}^{2}}} \right]\] \[=\underset{n\to \infty }{\mathop{\lim }}\,\,\frac{\Sigma n}{1-{{n}^{2}}}=\frac{1}{2}\,\,\underset{n\to \infty }{\mathop{\lim }}\,\,\,\,\frac{{{n}^{2}}+n}{1-{{n}^{2}}}=-\frac{1}{2}\].
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