A) ½
B) 0
C) 1
D) \[\infty \]
Correct Answer: A
Solution :
\[\underset{n\to \infty }{\mathop{\lim }}\,\,\left( \frac{1}{{{n}^{2}}}+\frac{2}{{{n}^{2}}}+\frac{3}{{{n}^{2}}}+.......+\frac{n}{{{n}^{2}}} \right)\] \[=\underset{n\to \infty }{\mathop{\lim }}\,\,\,\left( \frac{1+2+3+......+n}{{{n}^{2}}} \right)=\underset{n\to \infty }{\mathop{\lim }}\,\,\frac{\frac{n}{2}(n+1)}{{{n}^{2}}}\] \[=\frac{1}{2}\,\,\underset{n\to \infty }{\mathop{\lim }}\,\,\,\frac{n+1}{n}=\frac{1}{2}\,\,\underset{n\to \infty }{\mathop{\lim }}\,\,\,1+\frac{1}{n}=\frac{1}{2}\]
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