a,S=1.2+1.3+3.4+…+(n-1).n b,S=1.2.3+2.3.4+3.4.5+…+(n-2)(n-1)n

Question

a,S=1.2+1.3+3.4+…+(n-1).n
b,S=1.2.3+2.3.4+3.4.5+…+(n-2)(n-1)n

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Genesis 5 tháng 2021-07-21T09:30:20+00:00 2 Answers 7 views 0

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    0
    2021-07-21T09:31:27+00:00

    S=1.2+1.3+3.4+…+(n-1).n

    3S = 1.2.3 + 2.3.3 + 3.4.3 + … + (n – 1).3n

    3S = 1.2.3 + 2.3.(4 – 1) + 3.4.(5 – 2) + … + (n – 1).n.[(n + 1) – (n – 2)]

    3S = 1.2.3 + 2.3.4 – 1.2.3 + 3.4.5 – 2.3.4 + … + (n – 1).n.(n + 1) – (n – 2)(n – 1).n

    3S = n(n + 1)(n – 1)

    S=[ n.(n + 1)(n – 1)] :3

                   

     

    0
    2021-07-21T09:32:05+00:00

    Đáp án:

    Giải thích các bước giải:

    S=1.2+1.3+3.4+…+(n-1).n

    3S = 3.[ 1.2 + 2.3 + 3.4 + … + (n – 1).n]

    3S = 1.2.3 + 2.3.3 + 3.4.3 + … + (n – 1).n.3

    3S = 1.2.3 + 2.3.(4 – 1) + 3.4.(5 – 2) + … + (n – 1).n.[(n + 1) – (n – 2)]

    3S = 1.2.3 + 2.3.4 – 1.2.3 + 3.4.5 – 2.3.4 + … + (n – 1).n.(n + 1) – (n – 2)(n – 1).n

    3S = (n – 1)n(n + 1)

    S= (n – 1).n.(n + 1) : 3.

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