CHỨNG MINH A= 1/4 + 1/16 + 1/36 + 1/64 + 1/100 + 1/144+ 1/196 + 1/256 + 1 /324< 1/2 03/10/2021 Bởi Athena CHỨNG MINH A= 1/4 + 1/16 + 1/36 + 1/64 + 1/100 + 1/144+ 1/196 + 1/256 + 1 /324< 1/2
`1/4 + 1/16 + 1/36 + 1/64 + 1/100 + 1/144+ 1/196 + 1/256 + 1 /324` `= 1/4 (1 + 1/4 + 1/9 + 1/16 + 1/25 + 1/36 + 49 + 1/64 + 1/81)` `= 1/4 ( 1 + (1/2)^2 + (1/3)^2 + (1/4)^2 + (1/5)^2 + (1/6)^2 + (1/7)^2 + (1/8)^2 + (1/9)^2 ) ` `= 1/4 . (1 + 1/(1.2) + 1/(2.3) + 1/(3.4) + 1/(4.5) + 1/(5.6) + 1/(6.7) + 1/(6.8) + 1/(7.8) + 1/(8.9) )` `= 1/4 . (1 + 1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 +……. – 1/9)` `= 1/4 .( 2 – 1/9)` `= 1/4 . 17/9` `= 17/36 < 18/36 = 1/2` `=> A < 1/2` Bình luận
Đáp án: Giải thích các bước giải: Ta có : = 1/2·2 + 1/2·3 + 1/6·6 + 1/8.8 + 1/12·12 + 1/14·14 + 1/16·16 + 1/18.18 = 1/2 + 1/2 + 1/2 + 1/3 + … + 1/18 + 1/18 = 1/2 + (-1/2 + 1/2) + 1/3 + … + 1/18 + 1/18 = 1/2 + 0 + 1/3 + 0 + … + 0 + 0 = 1/2 + 1/3 = 3/6 + 2/6 = 5/6 ⇒ A < 5/6 < 1/2 Cho mình câu trả lời hay nhất nhé ! Bình luận
`1/4 + 1/16 + 1/36 + 1/64 + 1/100 + 1/144+ 1/196 + 1/256 + 1 /324`
`= 1/4 (1 + 1/4 + 1/9 + 1/16 + 1/25 + 1/36 + 49 + 1/64 + 1/81)`
`= 1/4 ( 1 + (1/2)^2 + (1/3)^2 + (1/4)^2 + (1/5)^2 + (1/6)^2 + (1/7)^2 + (1/8)^2 + (1/9)^2 ) `
`= 1/4 . (1 + 1/(1.2) + 1/(2.3) + 1/(3.4) + 1/(4.5) + 1/(5.6) + 1/(6.7) + 1/(6.8) + 1/(7.8) + 1/(8.9) )`
`= 1/4 . (1 + 1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 +……. – 1/9)`
`= 1/4 .( 2 – 1/9)`
`= 1/4 . 17/9`
`= 17/36 < 18/36 = 1/2`
`=> A < 1/2`
Đáp án:
Giải thích các bước giải:
Ta có :
= 1/2·2 + 1/2·3 + 1/6·6 + 1/8.8 + 1/12·12 + 1/14·14 + 1/16·16 + 1/18.18
= 1/2 + 1/2 + 1/2 + 1/3 + … + 1/18 + 1/18
= 1/2 + (-1/2 + 1/2) + 1/3 + … + 1/18 + 1/18
= 1/2 + 0 + 1/3 + 0 + … + 0 + 0
= 1/2 + 1/3
= 3/6 + 2/6
= 5/6
⇒ A < 5/6 < 1/2
Cho mình câu trả lời hay nhất nhé !