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

Toán Lớp 7: `A = (1 – 1/2) (1 – 1/4) (1 – 1/6) … (1 – 1/195)`. `text{CMR:}` `A < 1/14`

Home/ Toán Lớp 7: `A = (1 – 1/2) (1 – 1/4) (1 – 1/6) … (1 – 1/195)`. `text{CMR:}` `A < 1/14`

Toán Lớp 7: `A = (1 – 1/2) (1 – 1/4) (1 – 1/6) … (1 – 1/195)`. `text{CMR:}` `A < 1/14`

Tháng Hai 20, 2023 Toán học 1 Comment 0 views

Toán Lớp 7: A = (1 – 1/2) (1 – 1/4) (1 – 1/6) … (1 – 1/195).
text{CMR:} A < 1/14

Comments ( 1 )

  1. mocmien87
    mocmien87
    20 Tháng Hai, 2023 at 8:28 sáng
    Reply
    Giải đáp:
     A = (1 – 1/2)(1 – 1/4)(1 – 1/6)………………(1 – 1/195)
        =1/2 . 3/4 . 5/6 ……………. 194/195
    Mà 1/2 < 2/3 , 3/4 < 4/5 ,……,194/195<195/196
    ⇒ A < 2/3 . 4/5  …….. 195 / 196
    ⇒ A² < 1/2 . 2/3 . 3/4 . 4/5 …………. 194/195 . 195/196
    A² < 1/196
    ⇒ A² < (1/14)^2
    ⇒ A < 1/14 (đpcm)
     

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

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