Bài `1:`
`1/(1.2) + 1/(2.3) + 1/(3.4) + ... + 1/(99.100)`
`= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/99 - 1/100`
`= 1 - 1/100`
`= 99/100`
`--`
`(1 - 1/2) . (1 - 1/3) . (1 - 1/4) . ... . (1 - 1/2022)`
`= 1/2 . 2/3 . 3/4 . ... . 2021/2022`
`= (1.2.3. ... .2021)/(2.3.4. ... . 2022)`
`= 1/2022`
Bài `2:`
`(x + 1) + (x + 2) + (x + 3) + .... + (x + 5050) = 5050`
`=> (x + x + x + ... + x) + (1 + 2 + 3 + ... + 5050) = 5050`
`=> 5050 . x + [(5050 + 1) . 5050 : 2] = 5050`
`=> 5050 . x + 12753775 = 5050`
`=> 5050 . x = 5050 - 12753775`
`=> 5050 . x = -12748725`
`=> x = -12748725 : 5050`
`=> x = -2524,5`