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

Toán Lớp 10: Tính 1-1/2+1/3-1/4+…+1/(2n-1)-1/2n=1/(n+1)+1/(n+2)+…+1/2n

Tháng Một 16, 2023 Toán học 1 Comment 0 views

Toán Lớp 10: Tính 1-1/2+1/3-1/4+…+1/(2n-1)-1/2n=1/(n+1)+1/(n+2)+…+1/2n

Comments ( 1 )

  1. cobelolen
    cobelolen
    16 Tháng Một, 2023 at 8:49 chiều
    Reply
    Đề bài là chứng minh nhé
    Ta có:
    \qquad 1-1/2+1/3-1/4+…+1/{2n-1}-1/{2n}
    =(1+1/3+1/5+…+1/{2n-1})
    -(1/2+1/4+…+1/{2n})
    =(1+1/2+1/3+1/4+…+1/{2n-1}+1/{2n})
    -(1/2+1/4+…+1/{2n})-(1/2+1/4+…+1/{2n})
    =(1+1/2+1/3+1/4+…+1/{2n-1}+1/{2n})
    -2.(1/2+1/4+…+1/{2n})
    =(1+1/2+1/3+1/4+…+1/n+1/{n+1}+1/{n+2}+…+1/{2n-1}+1/{2n})
    -(1+1/2+…+1/{n})
    =1/{n+1}+1/{n+2}+…+1/{2n}
    Vậy: 1-1/2+1/3-1/4+…+1/{2n-1}-1/{2n}
    =1/{n+1}+1/{n+2}+…+1/{2n}

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

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