Chứng tỏ rằng ( 1-1/3 )(1-1/6)(1-1/15)…(1-1/253) < 2/5 Nhanh, chính xác, chi tiết nhé, k sao trên mạng 30/06/2021 Bởi Nevaeh Chứng tỏ rằng ( 1-1/3 )(1-1/6)(1-1/15)…(1-1/253) < 2/5 Nhanh, chính xác, chi tiết nhé, k sao trên mạng
`( 1 − 1/3 ) ( 1 − 1/6 ) . . . ( 1 − 1/253 )` `= 2/3 × 5/6 × . . . × 252/253` `= 4/6 × 10/12 × . . . ⋅ 504/506` `= (1 × 4)/(2 × 3) × (2 × 5)/(3 × 4) × . . . × (21 × 24)/(22 × 23)` `= (1 × 2 × 3 × 4^2 × 5^2 ⋅ . . . ⋅ 21^2 × 22 × 23 × 24)/(2 × 3^2 × 4^2 × . . . × 22^2 × 23)` `= (1 × 24)/(3 × 22)` `= 24/66 <2/5` `⇒ ( 1-1/3 )(1-1/6)(1-1/15)…(1-1/253) < 2/5` $#JAW#$ Bình luận
`( 1 − 1/3 ) ( 1 − 1/6 ) . . . ( 1 − 1/253 )`
`= 2/3 × 5/6 × . . . × 252/253`
`= 4/6 × 10/12 × . . . ⋅ 504/506`
`= (1 × 4)/(2 × 3) × (2 × 5)/(3 × 4) × . . . × (21 × 24)/(22 × 23)`
`= (1 × 2 × 3 × 4^2 × 5^2 ⋅ . . . ⋅ 21^2 × 22 × 23 × 24)/(2 × 3^2 × 4^2 × . . . × 22^2 × 23)`
`= (1 × 24)/(3 × 22)`
`= 24/66 <2/5`
`⇒ ( 1-1/3 )(1-1/6)(1-1/15)…(1-1/253) < 2/5`
$#JAW#$