Ta có ` 1/2^2 < 1/(1.2)`
` 1/3^2 < 1/(2.3)`
` 1/4^2 < 1/(3.4)`
` ...`
` 1/20^2 < 1/(19.20)`
`\to 1/2^2 +1/3^2+ 1/4^2 +... +1/20^2 < 1/(1.2) +1/(2.3) +1/(3.4) +... +1/(19.20)`
` 1/(1.2) +1/(2.3) +1/(3.4) +... +1/(19.20) = 1/1 - 1/2 +1/2 -1/3 + 1/3 -1/4 + .. +1/19 - 1/20`
` = 1 - 1/20 < 1`
`\to 1/2^2 +1/3^2+ 1/4^2 +... +1/20^2 < 1` hay ` A <1` (điều phải chứng minh)