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

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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

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Reese 4 tháng 2021-08-19T00:37:11+00:00 2 Answers 17 views 0

Answers ( )

    0
    2021-08-19T00:38:18+00:00

    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`

    0
    2021-08-19T00:39:09+00:00

    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`

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