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

Toán Lớp 7: tính tổng 1.2^2+2.3^2+3.4^2+…+99.100^2

Home/ Toán Lớp 7: tính tổng 1.2^2+2.3^2+3.4^2+…+99.100^2

Toán Lớp 7: tính tổng 1.2^2+2.3^2+3.4^2+…+99.100^2

Tháng Bảy 8, 2022 Toán học 2 Comments 0 views

Toán Lớp 7: tính tổng
1.2^2+2.3^2+3.4^2+…+99.100^2

Comments ( 2 )

  1. thaolanphuobg
    thaolanphuobg
    8 Tháng Bảy, 2022 at 7:39 sáng
    Reply
    Giải đáp:
    $25164150$
    Lời giải và giải thích chi tiết:
    $1.2^2+2.3^2+3.4^2\ +\,.\!.\!.+\ 99.100^2\\=1.2.2+2.3.3+3.4.4\ +\,.\!.\!.+\ 99.100.100\\=1.2.(3-1)+2.3.(4-1)+3.4.(5-1)\ +\,.\!.\!.+\ 99.100.(101-1)\\=1.2.3-1.2+2.3.4-2.3+3.4.5-3.4\ +\,.\!.\!.+\ 99.100.101-99.100\\=\bigg(\underbrace{1.2.3+2.3.4+3.4.5\ +\,.\!.\!.+\ 99.100.101}_{\large A}\bigg)-\bigg(\underbrace{1.2+2.3+3.4\ +\,.\!.\!.+\ 99.100}_{\large A’}\bigg)\\\Rightarrow A=1.2.3+2.3.4+3.4.5\ +\,.\!.\!.+\ 99.100.101\\\Rightarrow 4A=1.2.3.4+2.3.4.4+3.4.5.4\ +\,.\!.\!.+\ 99.100.101.4\\\Rightarrow4A=1.2.3.4+2.3.4.(5-1)+3.4.5.(6-2)\ +\,.\!.\!.+\ 99.100.101.(102-98)\\\Rightarrow 4A=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5\ +\,.\!.\!.+\ 99.100.101.102-98.99.100.101\\\Rightarrow 4A=(1.2.3.4+2.3.4.5+3.4.5.6\ +\,.\!.\!.+\ 99.100.101.102)-(1.2.3.4+2.3.4.5+3.4.5.6\ +\,.\!.\!.+\ 98.99.100.101)\\\Rightarrow 4A=99.100.101.102\\\Rightarrow A=25.99.101.102\\\Rightarrow A=25497450\\\Rightarrow A’=1.2+2.3+3.4\ +\,.\!.\!.+\ 99.100\\\Rightarrow3A’=1.2.3+2.3.3+3.4.3\ +\,.\!.\!.+\ 99.100.3\\\Rightarrow 3A’=1.2.3+2.3.(4-1)+3.4.(5-2)\ +\,.\!.\!.+\ 99.100.(101-98)\\\Rightarrow 3A’=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4\ +\,.\!.\!.+\ 99.100.101-98.99.100\\\Rightarrow 3A’=(1.2.3+2.3.4+3.4.5\ +\,.\!.\!.+\ 99.100.101)-(1.2.3+2.3.4+3.4.5\ +\,.\!.\!.+\ 98.99.100)\\\Rightarrow 3A’=99.100.101\\\Rightarrow A’=33.100.101\\\Rightarrow A’=333300\\=25497450-333300\\=25164150$

  2. ngoclanquynh
    ngoclanquynh
    8 Tháng Bảy, 2022 at 7:38 sáng
    Reply
    1.2^2+2.3^2+3.4^2+…+99.100^2
    = 1.2(3 – 1) + 2.3(4 – 1) + 3.4(5 – 1) + … + 99.100(101 – 1)
    = 1.2.3 – 1.2 + 2.3.4 – 2.3 + 3.4.5 – 3.4 + … + 99.100.101 – 99.100
    = (1.2.3 + 2.3.4 + 3.4.5 + … + 99.100.101)-(1.2 + 2.3 + 3.4 + … + 99.100)

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

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