Đáp án:
`(1 - 1/3) (1 - 1/6) (1 - 1/10) (1 - 1/15) ... (1 - 1/253)`
`= 2/3 × 5/6 × 9/10 × 14/15 × ... × 252/253`
`= (2 × 2)/(3 × 2) × (5 × 2)/(6 × 2) × (9 × 2)/(10 × 2) × (14 × 2)/(15 × 2) × ... × (252 × 2)/(253 × 2)`
`= 4/6 × 10/12 × 18/20 × 28/30 × ... × 504/506`
`= (4 × 10 × 18 × 28 × ... × 504)/(6 × 12 × 20 × 30 × ... × 506)`
`= (1 × 2×3×...×21)/(2×3×4...×22) × (4 ×5×6×...×24)/(3×4×5×...×23)`
`= 1/22 × 24/3`
`= 24/66`
`= 4/11`
`text{Ta thấy :}` `4/11 < 2/5`
`-> (1 - 1/3) (1 - 1/6) (1 - 1/10) (1 - 1/15) ... (1 - 1/253) < 2/5`
