Đáp án:
`9751/100`
Giải thích các bước giải:
`5/6+11/12+19/20+29/30+..........+9899/9900`
`=(1-1/6)+(1-1/12)+(1-1/20)+...+(1-1/9900)`
`=(1+1+1+...+1)-(1/6+1/12+1/20+...+1/9900)`
`=98-(1/2 .3+1/3 .4+1/4 .5+...+1/99 .100)`
`=98-(1/2 -1/3+1/3-1/4+1/4-1/5+...+1/99-1/100)`
`=98-(1/2 -1/100)`
`=98-\frac{50-1}{100}`
`=98-49/100`
`=\frac{9800-49}{100}`
`=9751/100`