`lim(\frac{1}{n²} + \frac{2}{n²} + ...+ \frac{n-1}{n²})`
Ta có:
`\frac{1}{n²} + \frac{2}{n²} + ...+ \frac{n-1}{n²}`
`= \ frac{1}{n²} (1+2+...+n-1)`
`=\frac{1}{n²}. \frac{(n-1)(1+n-1)}{2}`
`= \frac{(n-1)n}{2n²}`
`= \frac{n²-n}{2n²}`
`=> lim(\frac{1}{n²} + \frac{2}{n²} + ...+ \frac{n-1}{n²})`
`=lim \frac{n²-n}{2n²}`
`=lim \frac{1-\frac{1}{n}}{2}`
`= \frac{1-0}{2}`
`=\frac{1}{2}`