Toán Cho A=1/1x2x3+1/2x3x4+…+1/18x19x20. Chứng minh A < 1/4 Giúp mik vớiiii! 04/07/2021 By Valerie Cho A=1/1x2x3+1/2x3x4+…+1/18x19x20. Chứng minh A < 1/4 Giúp mik vớiiii!
`A= 1/(1.2.3) + 1/(2.3.4) + …+ 1/(18.19.20)` `A= 1/2 ( 1/1.2 – 1/2.3 + 1/2.3 – 1/3.4 +…+ 1/18.19 – 1/19.20)` `A= 1/2 ( 1/1.2 – 1/19.20)` `A= 1/2( 1/2 – 1/380)` `A= 1/4 – 1/760 < 1/4` Vậy `A < 1/4` Trả lời
Đáp án: `A=1/(1.2.3)+1/(2.3.4)+…+1/(18.19.20)` `=>2A=2/(1.2.3)+2/(2.3.4)+…+2/(18.19.20)` `=>2A=1/(1.2)-1/(2.3)+1/(2.3)+1/(3.4)+…+1/(18.19)-1/(19.20` `=>2A=1/(1.2)-1/(19.20)` `=>2A=1/2-1/19.20` `=>A=1/4-1/(2.19.20)<1/4` Vậy `A<1/4`. Trả lời
`A= 1/(1.2.3) + 1/(2.3.4) + …+ 1/(18.19.20)`
`A= 1/2 ( 1/1.2 – 1/2.3 + 1/2.3 – 1/3.4 +…+ 1/18.19 – 1/19.20)`
`A= 1/2 ( 1/1.2 – 1/19.20)`
`A= 1/2( 1/2 – 1/380)`
`A= 1/4 – 1/760 < 1/4`
Vậy `A < 1/4`
Đáp án:
`A=1/(1.2.3)+1/(2.3.4)+…+1/(18.19.20)`
`=>2A=2/(1.2.3)+2/(2.3.4)+…+2/(18.19.20)`
`=>2A=1/(1.2)-1/(2.3)+1/(2.3)+1/(3.4)+…+1/(18.19)-1/(19.20`
`=>2A=1/(1.2)-1/(19.20)`
`=>2A=1/2-1/19.20`
`=>A=1/4-1/(2.19.20)<1/4`
Vậy `A<1/4`.