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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 6: Mong các anh chị giúp em . Cho A = $\dfrac{1}{2}$ + $\dfrac{3}{2}$ + $(\dfrac{3}{2})^{2}$ + $(\dfrac{3}{2})^{3}$ + … $(\dfrac{3}{2})^

Toán Lớp 6: Mong các anh chị giúp em .
Cho A = $\dfrac{1}{2}$ + $\dfrac{3}{2}$ + $(\dfrac{3}{2})^{2}$ + $(\dfrac{3}{2})^{3}$ + … $(\dfrac{3}{2})^{2012}$ và B = $(\dfrac{3}{2})^{2013}$ : 2
Tính B – A
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Comments ( 1 )

  1. Giải đáp:

     B-A=-4*(3/2)^2013-1/2

    Lời giải và giải thích chi tiết:

     A= 1/2 + 3/2 + (3/2)^2 + (3/2)^3 + …. + (3/2)^2012

     A*3/2 = [1/2 + 3/2 + (3/2)^2 + (3/2)^3 + …. + (3/2)^2012]*3/2

     A*3/2 = 3/4 + (3/2)^2 + (3/2)^3 + …. + (3/2)^2012 + (3/2)^2013

     A*3/2 – A = [3/4 + (3/2)^2 + (3/2)^3 + …. + (3/2)^2012 + (3/2)^2013]-[1/2 + 3/2 + (3/2)^2 + (3/2)^3 + …. + (3/2)^2012]

     A*3/2-A*1 = 3/4+[(3/2)^2-(3/2)^2]+[(3/2)^3-(3/2)^3)]+…+[(3/2)^2012-(3/2)^2012]+(3/2)^2013-(1/2+3/2)

     A*(3/2-1)  = 3/4+(3/2)^2013-4/2

     A*1/2           = 3/4+(3/2)^2013-2

     A*1              = [3/4+3/2*(3/2)^2012]*2-2

     A*1              = 3/4*2 + 3/2*(3/2)^2012*2-2

     A                 = 6/4 + (3/2*2)*(3/2)^2012-2

     A                 = 3/2-2 + 3*(3/2)^2012

     A                 = 1/2 +  3*(3/2)^2012

    Mà B = (3/2)^2013:2

          B = 3/2*(3/2)^2012 : 2

          B = (3/2:2)*(3/2)^2012

          B = 3*(3/2)^2012:4

    => B-A =  3*(3/2)^2012:4 – [1/2 + 3*(3/2)^2012] 

    => B-A =  [3*(3/2)^2012:4-3*(3/2)^2012] – 1/2

    => B-A =  -3/4*3*(3/2)^2012-1/2

    => B-A =  -3/2*2*3*(3/2)^2012-1/2

    => B-A = -2*3*[3/2*(3/2)^2012]-1/2

    => B-A = -6*(3/2)^2012-1/2

    => B-A = -4*3/2*(3/2)^2012-1/2

    => B-A = -4*(3/2)^2013-1/2

    Vậy B-A =-4*(3/2)^2013-1/2

     

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222-9+11+12:2*14+14 = ? ( )

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