1/3 – 2/3^2 + 3/3^3 – 4/3^4 + … + 99/3^99 – 100/3^100 So sánh với 3/16

Question

1/3 – 2/3^2 + 3/3^3 – 4/3^4 + … + 99/3^99 – 100/3^100
So sánh với 3/16

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Ben Gia 5 years 2021-05-19T17:40:07+00:00 1 Answers 28 views 0

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  1. Nho
    0
    2021-05-19T17:41:22+00:00
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    Đáp án:

     A<3/16

    Giải thích các bước giải:

    Đặt A=1/3-2/3^2+3/3^3-4/3^4+…+99/3^99-100/3^100

    3A=1-2/3+3/3^2-4/3^3+…+99/3^98-100/3^99

    3A+A=1-1/3+1/3^2-1/3^3+1/3^4-…+1/3^98-1/3^99-100/3^100 <1-1/3+1/3^2+1/3^3+1/3^4-…+1/3^98-1/3^99

    Đặt S=1-1/3+1/3^2-1/3^3+1/3^4-…+1/3^98-1/3^99

    3S=3-1+1/3-1/3^2+1/3^3-…-1/3^98

    3S+S=3-1/3^99

    S=(3-1/3^99) :4

    S=3/4-1/4.3^99 

    ⇒4A<3/4-1/4.3^99 

    ⇒A<(3/4-1/4.3^99):4 

    ⇒A<3/16-1/16.3^99<3/16 Vậy 1/3-2/3^2+3/3^3-4/3^4+…+99/3^99-100/3^100<3/16

    CHÚC BẠN HỌC TỐT :3

    đánh giá 5 sao và câu tlhn nhé

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