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

Question

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

in progress 0
Kim Chi 3 years 2021-05-14T13:16:41+00:00 1 Answers 47 views 0

Answers ( )

  1. Cherry
    0
    2021-05-14T13:17:59+00:00
    Reply

    Đáp án:

     

    Giải thích các bước giải:

    Ta có: A=1/3 – 2/3^2+3/3^3 – 4/3^4+ … – 100/3^100
    =>3A=1 -2/3 +3/3^2 – 4/3^3+ … – 100/3^99
    =>4A=A+3A=1-1/3+1/3^2-1/3^3+…-1/3^99 – 100/3^100
    =>12A=3.4A=3-1+1/3-1/3^2+…-1/3^98 – 100/3^99
    =>16A=12A+4A=3-1/3^99-100/3^99-100/3^1…
    <=> 16A=3-101/3^99-100/3^100
    <=> A=3/10-(101/3^99+100/3^100)/16 < 3/10
    Suy ra A<3/10

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )