`S= 1/2022 - (5/2.4 + 5/4.6 +...+5/2020.2022)`
Đặt `A= 5/2.4 + 5/4.6 +...+5/2020.2022`
`A: 5 = 1/2.4 + 1/4.6 +...+1/2020.2022`
`A:5 .2 = 2/2.4 + 2/4.6 +...+2/2020.2022`
`A:5.2 = 1/2 - 1/4 + 1/4 - 1/6 +...+ 1/2020 - 1/2022`
`A:5.2 = 1/2- 1/2022`
`A:5.2= 505/1011`
`A:5 = 505/1011 : 2`
`A:5=505/2022 `
`A= 505/2022 .5`
`A=2525/2022`
`=> S = 1/2022 - 2525/2022`
`=> S= -1262/1011`
Vậy `S= -1262/1011`