`1/(1 xx 2) + 1/(2 xx 3) +1/(3 xx4) +....+ 1/(2021 xx 2022)`
`= (2-1)/(1xx2) + (3-2)/(2 xx3)+ (4-3)/(3 xx4) +...+ (2022 - 2021)/(2021 xx 2022)`
`= 1/1- 1/2 + 1/2 - 1/3 + 1/3 - 1/4+...+1/2021 - 1/2022`
`= 1 - 1/2022`
`= 2022/2022 - 1/2022`
`= 2021/2022`