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

Toán Lớp 6: 1+1/3+1/6+1/10+-…+2/Xx(X+1)=1 1989/1991 1 1989/1991 là 1 1989 phần 1991

Tháng Hai 22, 2023 Toán học 2 Comments 0 views

Toán Lớp 6: 1+1/3+1/6+1/10+…….+2/Xx(X+1)=1 1989/1991
1 1989/1991 là 1 1989 phần 1991

Comments ( 2 )

  1. minhtuquynh
    minhtuquynh
    22 Tháng Hai, 2023 at 10:56 sáng
    Reply
    Giải đáp:
    $\\$
    1 + 1/3 + 1/6 + 1/10 + … +2/(x (x + 1) ) = 1 1989/1991
    ↔ 2/2 + 2/6 + 2/12 + 2/20 + … + 2/(x (x + 1) ) = 3980/1991
    ↔ 2 × [1/2 + 1/6 +  … + 1/(x (x+1) )] = 3980/1991
    ↔ 2 × [1/(1×2) + 1/(2×3) +  … + 1/(x (x+1) )] = 3980/1991
    ↔ 2 × [1 – 1/2 + 1/2 – 1/3 + … + 1/x – 1/(x+1)] = 3980/1991
    ↔ 2 × [1 + (- 1/2 + 1/2 – 1/3 + … + 1/x) – 1/(x+1)] = 3980/1991
    ↔ 2 × [1 – 1/(x+1)] = 3980/1991
    ↔ 1 – 1/(x+1) = 3980/1991 ÷ 2
    ↔ 1 – 1/(x+1) = 3980/1991 × 1/2
    ↔ 1 – 1/(x+1) = 1990/1991
    ↔ 1/(x+1) =1-1990/1991
    ↔1/(x+1)=1991/1991 – 1990/1991
    ↔1/(x+1) = 1/1991
    ↔ x+1=1991
    ↔x=1991-1
    ↔x=1990
    Vậy x=1990
     

  2. hoquyly
    hoquyly
    22 Tháng Hai, 2023 at 10:55 sáng
    Reply
    Giải đáp + Lời giải và giải thích chi tiết:
    1+1/3+1/6+…+2/(x.(x+1))=1 1989/1991
    =>2/2+2/6+2/12+…+2/(x.(x+1))=3980/1991
    =>2/1.2+2/2.3+2/3.4+…+2/(x.(x+1))=3980/1991
    =>2(1/1.2+1/2.3+1/3.4+…+1/(x.(x+1))=3980/1991
    =>2(1-1/2+1/2-1/3+1/3-1/4+…+1/x-1/(x+1))=3980/1991
    =>2(1-1/(x+1))=3980/1991
    =>1-1/(x+1)=3980/1991:2
    =>1-1/(x+1)=3980/1991. 1/2
    =>1-1/(x+1)=1990/1991
    =>1/(x+1)=1-1990/1991
    =>1/(x+1)=1991/1991-1990/1991
    =>1/(x+1)=1/1991
    =>x+1=1991
    =>x=1991-1
    =>x=1990

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

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