Tính nhanh `1/100.99` - `1/99.98` - .... - `1/3.2` - `1/2.1`
2 câu trả lời
`1/100.99` - `1/99.98` - `1/98.97` -...- `1/3.2` - `1/2.1`
`=` `-` ( `1/100.99` + `1/99.98` + `1/98.97` +...+ `1/3.2` + `1/2.1` )
`=` `-` ( `1/2.1` + `1/3.2` +...+ `1/98.97` + `1/99.98` + `1/100.99` )
`=` `-` ( `1/1.2` + `1/2.3` + `1/3.4` +...+ `1/97.98` + `1/98.99` + `1/99.100` )
`=` `-` ( `1/1` - `1/2` + `1/2` - `1/3` + `1/3`......- `1/98` + `1/98` - `1/99` + `1/99` - `1/100` )
`=` `-` ( `1/1` - `1/100` )
`=` `-` `99/100`
Đáp án:
` (-9799)/(9900)`
Giải thích các bước giải:
`1/(100 . 99) -1/(99 . 98) - ... - 1/(3 .2) -1/(2 .1)`
`= 1/(100.99) -(1/(98 . 99) + ... + 1/(2 .3)+1/(1.2) )`
`= 1/(100 . 99) - (1/(1.2)+1/(2.3)+... +1/(98 .99))`
`= 1/(100 . 99) -(1 -1/2+1/2-1/3+ ... +1/98 -1/99)`
`= 1/(100 . 99) - (1 - 1/99)`
`= 1/(100 . 99) - 98/99`
`= 1/(99 . 100) - (9800)/(99 . 100)`
`= (-9799)/(9900)`
