Đáp án:
`A = 2/(1 × 5) + 3/(5 × 11) + 4/(11 × 19) + 5/(19 × 29) + 6/(29 × 41)`
`⇔ 2 × A = 2 × (2/(1 × 5) + 3/(5 × 11) + 4/(11 × 19) + 5/(19 × 29) + 6/(29 × 41) )`
`⇔ 2 × A = 4/(1 × 5) + 6/(5 × 11) + 8/(11 × 19) + 10/(19 × 29) + 12/(29 × 41)`
`⇔ 2 × A = 1 - 1/5 + 1/5 - 1/11 + 1/11 - 1/9 + 1/19 - 1/29 + 1/29 - 1/41`
`⇔ 2 × A = 1 + (- 1/5 + 1/5 - 1/11 + 1/11 - 1/9 + 1/19 - 1/29 + 1/29) - 1/41`
`⇔ 2 × A = 1 - 1/41`
`⇔ 2 × A = 40/41`
`⇔ A = 40/41 ÷ 2`
`⇔ A=20/41`
`text{Vậy}` `A = 20/41`
