Bài $ 7 $. Thu gọn tổng sau: $ A $ $ = $ $ 1 + 3 + $ $3^{2} + $ $3^{3} + $ $ ….. + $ $3^{100}$

Question

Bài $ 7 $. Thu gọn tổng sau:
$ A $ $ = $ $ 1 + 3 + $ $3^{2} + $ $3^{3} + $ $ ….. + $ $3^{100}$

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Eirian 4 years 2020-11-11T15:22:04+00:00 2 Answers 78 views 0

Answers ( )

  1. Bo
    0
    2020-11-11T15:23:43+00:00
    Reply

    Ta có: `A = 1 + 3 + 3^2 + … + 3^100`

    `3A = 3 + 3^2 + 3^3 + … + 3^101`

    `→ 3A – A = 3^101 – 1`

    `→ 2A = 3^101 – 1`

    `→ A = (3^101 – 1)/2`

     

  2. Jezebel
    0
    2020-11-11T15:23:59+00:00
    Reply

    $ A=1 +3+3^2 + 3^3 + …..+3^{100}$

    $3A = 3 + 3^2 + 3^3 + 3^4 + …..+ 3 ^{101}$

    Ta lấy :

    $ 3A-A   =( 3 + 3^2 + 3^3 + 3^4 + …..+ 3 ^{101})-(1 +3+3^2 + 3^3 + …..+3^{100} )$

    $2A = 3 ^{101}$ -1

    A = A = $\dfrac{3^{101}-1}{2}$ 

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