ta có :
`\frac{1}{1 xx 2} = 1 - 1/2`
`\frac{1}{2 xx 3} = 1/2 - 1/3`
`\frac{1}{3 xx 4} = 1/3 - 1/4`
`\frac{1}{4xx5} = 1/4 - 1/5`
`\frac{1}{5xx6}= 1/5 - 1/6`
`\frac{1}{6xx7} = 1/6 - 1/7`
................
`\frac{1}{9 xx 10} = 1/9 - 1/10`
`\frac{1}{10xx11} = 1/10 - 1/11`
⇒`\frac{1}{1 xx 2} +\frac{1}{2 xx 3} + \frac{1}{3 xx 4}+ \frac{1}{4xx5} +\frac{1}{5xx6} + \frac{1}{6xx7} + ....... +\frac{1}{9 xx 10} +\frac{1}{10xx11}`
`=1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + ..... + 1/9 - 1/10 + 1/10 - 1/11`
`= 1 - 1/11`
`= 11/11 - 1/11`
`= 10/11`
