tính: $\frac{5}{3.4}$+$\frac{5}{4.6}$+ $\frac{5}{5.8}$+$\frac{5}{6.10}$+…+ $\frac{5}{40.78}$

Question

tính:
$\frac{5}{3.4}$+$\frac{5}{4.6}$+ $\frac{5}{5.8}$+$\frac{5}{6.10}$+…+ $\frac{5}{40.78}$

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Caroline 4 tháng 2021-08-25T07:29:56+00:00 2 Answers 8 views 0

Answers ( )

    0
    2021-08-25T07:30:57+00:00

    Đáp án:

    `A=19/16`

    Giải thích các bước giải:

    `A=5/3.4+5/4.6+5/5.8+5/6.10+…+5/40.78`

    `2A=5.2/3.4+5.2/4.6+5.2/5.8+5.2/6.10+…+5.2/40.78`

    `2A=5/2.3+5/3.4+5/4.5+5/5.6+…+5/39.40`

    `2A=5(1/2.3+1/3.4+1/4.5+1/5.6+…+1/39.40)`

    `2A=5(1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+…+1/39-1/40)`

    `2A=5(1/2-1/40)`

    `2A=5*19/40`

    `2A=19/8`

    `A=19/16`

     

    0
    2021-08-25T07:31:10+00:00

    $#Đáp án+Giải thích các bước giải:$

    Đặt : `A = 5/(3*4)+5/(4*6)+5/(5*8)+5/(6*10)+…+5/(40*78)`

    `=> 2A = (5*2)/(3*4)+(5*2)/(4*6)+(5*2)/(5*8)+(5*2)/(6*10)+…+(5*2)/(40*78)`

    `=> 2A = 5/(2*3)+5/(3*4)+5/(4*5)+5/(5*6)+…+5/(39*40)`

    `=> 2A = 1 – (1/2-1/3+1/3-1/4+1/4-1/5+…+1/39-1/40)`

    `=> 2A = 5*(1/2-1/40)`

    `=> 2A = 5*19/40`

    `=> 2A = 19/8`

    `=> A = 19/8 ÷ 2`

    `=> A = 19/16`

    Vậy `A=19/16`

    $#Cam$

    $#XIN HAY NHẤT CHO NHÓM AK$

     

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