MCQ
$\mathop {\lim }\limits_{n \to \infty } \left\{ {\frac{1}{{{n^2}}} + \frac{2}{{{n^2}}} + \frac{3}{{{n^2}}} + ...... + \frac{n}{{{n^2}}}} \right\}$ is
- ✓$1/2$
- B$0$
- C$1$
- D$\infty $
$ = \mathop {\lim }\limits_{n \to \infty } \,\,\left( {\frac{{1 + 2 + 3 + ...... + n}}{{{n^2}}}} \right) = \mathop {\lim }\limits_{n \to \infty } \,\frac{{\frac{n}{2}(n + 1)}}{{{n^2}}}$
$ = \frac{1}{2}\,\,\mathop {\lim }\limits_{n \to \infty } \,\,\frac{{n + 1}}{n} = \frac{1}{2}\,\,\mathop {\lim }\limits_{n \to \infty } \,\,1 + \frac{1}{n} = \frac{1}{2}$
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