Toán 1tính nhanh A=(1/2+5/6+11/12+19/20+……+89/90)*100 2.tìm x biết :a,17-(8 và 1/2-x)=12 19/08/2021 By Reese 1tính nhanh A=(1/2+5/6+11/12+19/20+……+89/90)*100 2.tìm x biết :a,17-(8 và 1/2-x)=12
1. Đặt `B = 1/2 + 5/6 + 11/12 + 19/20 + … + 89/90` `⇒ B = (1 – 1/2) + (1 – 1/6) + (1 – 1/12) + (1 – 1/20) + … + (1 – 1/90)` `= (1 + 1 + 1 + 1 + … + 1) – (1/2 + 1/6 + 1/12 + 1/20 + … + 1/90)` `= 1 . 9 – (1/(1.2) + 1/(2.3) + 1/(3.4) + 1/(4.5) + … + 1/(9.10))` `= 9 – (1 – 1/2 + 1/2 – 1/3 + 1/3 – 11/4 + 1/4 – 1/5 + 1/5 – 1/6 + … + 1/9 – 1/10)` `= 9 – (1 – 1/10)` `= 9 – 9/10 = 81/10` `⇒ A = 81/10 . 100 = 810` Vậy `A = 810` 2. `17 – (8 1/2 – x) = 12` `⇒ 17 – (17/2 – x) = 12` `⇒ 17 – 17/2 + x = 12` `⇒ x = 12 + 17/2 – 17` `⇒ x = 7/2` Vậy `x = 7/2` Trả lời
Đáp án: `A = 810` `x = 7/2` Giải thích các bước giải: `A = ( 1/2+5/6+11/12+…+89/90 ) . 100` Đặt `B= 1/2+5/6+11/12+…+89/90` `= 1-1/2+1-1/6+1-1/12+…+1-1/90` `= (1+1+1+…+1)-(1/2+1/6+1/12+…+1/90)` `= 9 – ( 1/1.2 + 1/2.3 + 1/3.4 + … + 1/9.10 )` `= 9 – (1/1-1/2+1/2-1/3+1/3-1/4+…+1/9-1/10)` `= 9 – (1/1-1/10) = 81/10` `to A = 81/10 . 100 = 810` $\\$ `2)` `17 – ( 8 1/2 – x ) = 12` `to 17/2 – x = 17 – 12` `to 17/2 – x = 5` `to x = 17/2 – 5` `to x = 7/2` Vậy `x = 7/2` Trả lời
1. Đặt `B = 1/2 + 5/6 + 11/12 + 19/20 + … + 89/90`
`⇒ B = (1 – 1/2) + (1 – 1/6) + (1 – 1/12) + (1 – 1/20) + … + (1 – 1/90)`
`= (1 + 1 + 1 + 1 + … + 1) – (1/2 + 1/6 + 1/12 + 1/20 + … + 1/90)`
`= 1 . 9 – (1/(1.2) + 1/(2.3) + 1/(3.4) + 1/(4.5) + … + 1/(9.10))`
`= 9 – (1 – 1/2 + 1/2 – 1/3 + 1/3 – 11/4 + 1/4 – 1/5 + 1/5 – 1/6 + … + 1/9 – 1/10)`
`= 9 – (1 – 1/10)`
`= 9 – 9/10 = 81/10`
`⇒ A = 81/10 . 100 = 810`
Vậy `A = 810`
2. `17 – (8 1/2 – x) = 12`
`⇒ 17 – (17/2 – x) = 12`
`⇒ 17 – 17/2 + x = 12`
`⇒ x = 12 + 17/2 – 17`
`⇒ x = 7/2`
Vậy `x = 7/2`
Đáp án:
`A = 810`
`x = 7/2`
Giải thích các bước giải:
`A = ( 1/2+5/6+11/12+…+89/90 ) . 100`
Đặt `B= 1/2+5/6+11/12+…+89/90`
`= 1-1/2+1-1/6+1-1/12+…+1-1/90`
`= (1+1+1+…+1)-(1/2+1/6+1/12+…+1/90)`
`= 9 – ( 1/1.2 + 1/2.3 + 1/3.4 + … + 1/9.10 )`
`= 9 – (1/1-1/2+1/2-1/3+1/3-1/4+…+1/9-1/10)`
`= 9 – (1/1-1/10) = 81/10`
`to A = 81/10 . 100 = 810`
$\\$
`2)`
`17 – ( 8 1/2 – x ) = 12`
`to 17/2 – x = 17 – 12`
`to 17/2 – x = 5`
`to x = 17/2 – 5`
`to x = 7/2`
Vậy `x = 7/2`