`1/1.2+1/2.3+1/3.4+...+1/999.1000`
`= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +...+ 1/999 - 1/1000`
`= 1 - 1/1000 < 1`
`1/(2²) + 1/(3²) + 1/(4²) +...+ 1/(2020²)`
`< 1/1.2 + 1/2.3 + 1/3.4 +...+ 1/2019.2020`
`= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +...+ 1/2019 - 1/2020`
`= 1 - 1/2020 < 1`