cho a=1+3+3 mũ 2+3 mũ 3+3 mũ 4+…..+3 mũ 7

Question

cho a=1+3+3 mũ 2+3 mũ 3+3 mũ 4+…..+3 mũ 7

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Charlie 4 tuần 2021-07-08T20:07:13+00:00 2 Answers 3 views 0

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    0
    2021-07-08T20:08:17+00:00

    Đáp án:

     

    Giải thích các bước giải:

     a = 1 + 3 + 3$x^{2}$ + 3$x^{3}$ + $3^{4}$ + $3^{5}$ + $3^{6}$ + $3^{7}$ 

    ⇒3a = 3 + 3$x^{2}$ + 3$x^{3}$ + 3$x^{4}$ + 3$x^{5}$ + 3$x^{6}$ 

    ⇒3a – a = 3 + 3$x^{2}$ + 3$x^{3}$ + 3$x^{4}$ + 3$x^{5}$ + 3$x^{6}$ – ( 1 + 3 + 3$x^{2}$ + 3$x^{3}$ + $3^{4}$ + $3^{5}$ + $3^{6}$ + $3^{7}$  )

    ⇒ 2a = 3 + 3$x^{2}$ + 3$x^{3}$ + 3$x^{4}$ + 3$x^{5}$ + 3$x^{6}$ – 1 – 3 – 3$x^{2}$ – 3$x^{3}$ – $3^{4}$ – $3^{5}$ – $3^{6}$ – $3^{7}$ 

    ⇒2a = (3-3) + ( 3$x^{2}$ – 3$x^{2}$) + (3$x^{3}$ – 3$x^{3}$) + (3$x^{4}$ – 3$x^{4}$) + (3$x^{5}$ -3$x^{5}$ ) + (3$x^{6}$ – 3$x^{6}$) – $3^{7}$ -1

    ⇒ 2a = 3$x^{7}$ – 1

    ⇒ a = $\frac{3x^{7} – 1}{2}$ 

    0
    2021-07-08T20:09:12+00:00

    Vì A = 1 + 3 + 3^2 + 3^3 + 3^4 + … + 3^7

    => 3A = 3 + 3^2 + 3^3 + 3^4 + … + 3^8

    => 3A – A = (3 + 3^2 + 3^3 + 3^4 + … + 3^8) – (1 + 3 + 3^2 + 3^3 + 3^4 + … + 3^7)

    => 2A = 3^8 – 1

    => A = 3^8 – 1 / 2

    @vietdorapan

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