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

Toán Lớp 7: Chứng minh rằng `1/2 . 3/4 . 5/6 – 99/100 < 1/10`

Tháng Ba 13, 2023 Toán học 2 Comments 0 views

Toán Lớp 7: Chứng minh rằng 1/2 . 3/4 . 5/6 …. 99/100 < 1/10

Comments ( 2 )

  1. ngocbichchau
    ngocbichchau
    13 Tháng Ba, 2023 at 11:16 sáng
    Reply
    Đặt A = 1/2 . 3/4 . 5/6 …. 99/100
    Ta có : 1/2 < 2/3 , 3/4 < 4/5 , 5/6 < 6/7, …. , 99/100 < 100/101
    ⇒ 1/2 . 3/4 . 5/6 …. 99/100 < 2/3 . 4/5 . 6/7 …. 100/101
    ⇒ S < 2/3 . 4/5 . 6/7 …. 100/101
    ⇒ S^2 < ( 1/2 . 3/4 . 5/6 …. 99/100 ) . ( 2/3 . 4/5 . 6/7 …. 100/101 )
    ⇒ S^2 < 1/2 . 2/3 . 3/4 . 4/5 …. 99/100 . 100/101
    ⇒ S^2 < ( 1 . 2 . 3 . 4 …. 99 . 100 )/( 2 . 3 . 4 . 5 …. 101 )
    ⇒ S^2 < 1/101 < 1/100
    Do S^2 < 1/100 ⇒ S < 1/10
    ⇒ 1/2 . 3/4 . 5/6 …. 99/100 < 1/10 ( Điều phải chứng minh )

  2. quynhmaithu
    quynhmaithu
    13 Tháng Ba, 2023 at 11:16 sáng
    Reply
    Đặt:
    A = 1/2 . 3/4 . 5/6 . …. . 99/100
    Có:
    1/2 < 2/3
    3/4 < 4/5
    5/6 < 6/7
    …
    99/100 < 100/101
    => A < 2/3 . 4/5 . 6/7 . … . 100/101
    => A . A < (1/2 . 3/4 . 5/6 . …. . 99/100) . (2/3 . 4/5 . 6/7 . … . 100/101)
    => A^2 < 1/2 . 2/3 . 3/4 . 4/5 . … . 100/101
    => A^2 < 1/100
    => A < 1/10 (Đpcm)
    Vậy 1/2 . 3/4 . 5/6 . …. . 99/100 < 1/10
     

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

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