A = 8/3.7 + 8/7.11 + 8/11.15 + … + 8/97.101

Question

A = 8/3.7 + 8/7.11 + 8/11.15 + … + 8/97.101

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Đan Thu 9 months 2021-04-29T00:31:50+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-04-29T00:33:03+00:00

    *Lời giải :

    `A = 8/(3.7) + 8/(7.11) + 8/(11.15) + … + 8/(97 . 101)`

    `⇔ A = 2 . [1/3 – 1/7 + 1/7 – 1/11 + 1/11 – 1/15 + .. .+ 1/97 – 1/101]`

    `⇔ A = 2 [1/3 + (- 1/7 + 1/7 – 1/11 + 1/11 – 1/15 + .. .+ 1/97) – 1/101]`

    `⇔ A = 2 . [1/3 – 1/101]`

    `⇔ A = 2 . 98/303`

    `⇔ A = 196/303`

    Vậy `A = 196/303`

    0
    2021-04-29T00:33:10+00:00

    $\text{Đáp án + Giải thích các bước giải:}$

    `A=(8)/(3.7)+(8)/(7.11)+(8)/(11.15)+…+(8)/(97.101)`

    `=>(A)/(2)=(4)/(3.7)+(4)/(7.11)+(4)/(11.15)+…+(4)/(97.101)`

    `=>(A)/(2)=(1)/(3)-(1)/(7)+(1)/(7)-(1)/(11)+(1)/(11)-(1)/(15)+…+(1)/(97)-(1)/(101)`

    `=>(A)/(2)=(1)/(3)-(1)/(101)`

    `=>(A)/(2)=(98)/(303)`

    `=>A=(196)/(303)`

     

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