Đáp án:
`(x - 1/2) + (x - 1/6) + (x - 1/12) + (x - 1/20) + ... + (x - 1/90) + (x - 1/110) = 12/11`
`⇔ x - 1/2 + x - 1/6 + x - 1/12 + x - 1/20 + ... + x - 1/90 + x - 1/110 = 12/11`
`⇔ (x + x + x + x + ... + x + x) - (1/2 + 1/6 + 1/12 + 1/20 + ... + 1/90 + 1/110) = 12/11`
`⇔ 10x - (1/2 + 1/6 + 1/12 + 1/20 + ... + 1/90 + 1/110) = 12/11 (1)`
Xét `1/2 + 1/6 + 1/12 + 1/20 + ... + 1/90 + 1/110`
`= 1/(1 × 2) + 1/(2 × 3) + 1/(3 × 4) + 1/(4 × 5) + ... + 1/(9 × 10) + 1/(10 × 11)`
`= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/9 - 1/10 + 1/10 - 1/11`
`= 1 + (- 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/9 - 1/10 + 1/10) - 1/11`
`= 1 - 1/11`
`= 10/11`
Thay vào `(1)` ta được :
`⇔ 10x - 10/11 = 12/11`
`⇔ 10x = 12/11 + 10/11`
`⇔ 10x = 2`
`⇔ x = 2 ÷ 10`
`⇔ x = 1/5`
Vậy `x = 1/5`
