Toán Chứng minh : A = 1/1×3 + 1/2×4 + 1/3×5 + 1/4×6 + … + 1/97×99 + 1/98×100 < 3/4 17/09/2021 By Kaylee Chứng minh : A = 1/1×3 + 1/2×4 + 1/3×5 + 1/4×6 + … + 1/97×99 + 1/98×100 < 3/4
Đáp án: `A<3/4` Giải thích các bước giải: `A=1/(1.3)+1/(2.4)+1/(3.5)+…+1/(97.99)+1/(98.100)` `=1/2 . (2/(1.3)+2/(2.4)+2/(3.5)+…+2/(97.99)+2/(98.100))` `=1/2 . (1/1-1/3+1/2-1/4+1/3-1/5+…+1/97-1/99+1/98-1/100)` `=1/2 . (1+1/2-1/99-1/100) = 1/2 . (3/2-1/99-1/100) = 3/4 -1/(99.2)-1/(100.2) < 3/4` `to đpcm` Trả lời
`A = 1/1.3 + 1/2.4 + 1/3.5 + 1/4.6 + … + 1/97.99 + 1/98.100``=> 2.A = 2.(1/1.3 + 1/2.4 + 1/3.5 + 1/4.6 + … + 1/97.99 + 1/98.100)` `=> 2.A = 2/1.3 + 2/2.4 + 2/3.5 + 2/4.6 + …+ 2/97.99 + 2/98.100``=> 2.A = 1-1/3 +1/2 – 1/4 + 1/3 -1/5 +1/4-1/6 +…+1/97-1/99 + 1/98-1/100``=> 2.A = 1+1/2 -1/99 -1/100``=> 2.A < 1 /4 + 1/2 – 1/99 – 1/100 (do\ 1/4 <1)``=> 2.A < 3/4 – 1/99 – 1/100``=> 2.A < 3/4` `=> A < 3/8 < 3/4``=> A < 3/4` Trả lời
Đáp án:
`A<3/4`
Giải thích các bước giải:
`A=1/(1.3)+1/(2.4)+1/(3.5)+…+1/(97.99)+1/(98.100)`
`=1/2 . (2/(1.3)+2/(2.4)+2/(3.5)+…+2/(97.99)+2/(98.100))`
`=1/2 . (1/1-1/3+1/2-1/4+1/3-1/5+…+1/97-1/99+1/98-1/100)`
`=1/2 . (1+1/2-1/99-1/100) = 1/2 . (3/2-1/99-1/100) = 3/4 -1/(99.2)-1/(100.2) < 3/4`
`to đpcm`
`A = 1/1.3 + 1/2.4 + 1/3.5 + 1/4.6 + … + 1/97.99 + 1/98.100`
`=> 2.A = 2.(1/1.3 + 1/2.4 + 1/3.5 + 1/4.6 + … + 1/97.99 + 1/98.100)`
`=> 2.A = 2/1.3 + 2/2.4 + 2/3.5 + 2/4.6 + …+ 2/97.99 + 2/98.100`
`=> 2.A = 1-1/3 +1/2 – 1/4 + 1/3 -1/5 +1/4-1/6 +…+1/97-1/99 + 1/98-1/100`
`=> 2.A = 1+1/2 -1/99 -1/100`
`=> 2.A < 1 /4 + 1/2 – 1/99 – 1/100 (do\ 1/4 <1)`
`=> 2.A < 3/4 – 1/99 – 1/100`
`=> 2.A < 3/4`
`=> A < 3/8 < 3/4`
`=> A < 3/4`