S = 1x2 + 2x3 + 3x4 + ……………… + 11x12 + 12x13
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
S = 1x2 + 2x3 + 3x4 + ……………… + 11x12 + 12x13
3S=1x2x3 + 2x3x3 + 3x4x3+ ………. + 11x12x3 + 12x13x3
Ta lấy K = 1x2x3 +2x3x4 + 3x4x5 + …… + 11x12x13 + 12x13x14
- 3S = 1x2x3 + 2x3x3 + 3x4x3+ ……… + 11x12x3 + 12x13x3
------------------------------------------------------------------------------------
K – 3S = 0 + 2x3x1 + 3x4x2 + …… .. + 11x12x10 + 12x13x11
K – 3S = K – 12x13x14
Từ đó suy ra: 3S = 12x13x14
S = 4x13x14 = 728
Cách 2:
S x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + …. + 11x12x(13-10) + 12x13x(14-11)
S x 3 = 1x2x3 + 2x3x4 – 2x3x1 + 3x4x5 – 3x4x2 + …..+ 11x12x13 – 11x12x10 +12x13x14 – 12x13x11
S x 3 = 12 x 13 x14
S = 4 x 13 x 14
S = 728
![](https://rs.olm.vn/images/avt/0.png?1311)
3C = 1x2x3 + 2x3x(4-1) + ... + 11x12x(13-9)
3C = 1x2x3 + 2x3x4 - 1x2x3 + ... + 11x12x13 - 9x11x12
3C = 9x11x12
3C = 1188
C = 396
![](https://rs.olm.vn/images/avt/0.png?1311)
S = 1x2 + 2x3 + 3x4 + ……………… + 11x12 + 12x13
3S=1x2x3 + 2x3x3 + 3x4x3+ ………. + 11x12x3 + 12x13x3
Ta lấy K = 1x2x3 +2x3x4 + 3x4x5 + …… + 11x12x13 + 12x13x14
- 3S = 1x2x3 + 2x3x3 + 3x4x3+ ……… + 11x12x3 + 12x13x3
------------------------------------------------------------------------------------
K – 3S = 0 + 2x3x1 + 3x4x2 + …… .. + 11x12x10 + 12x13x11
K – 3S = K – 12x13x14
Từ đó suy ra: 3S = 12x13x14
S = 4x13x14 = 728
![](https://rs.olm.vn/images/avt/0.png?1311)
Cách 1:
S = 1x2 + 2x3 + 3x4 + ……………… + 11x12 + 12x13
3S=1x2x3 + 2x3x3 + 3x4x3+ ………. + 11x12x3 + 12x13x3
Ta lấy K = 1x2x3 +2x3x4 + 3x4x5 + …… + 11x12x13 + 12x13x14
- 3S = 1x2x3 + 2x3x3 + 3x4x3+ ……… + 11x12x3 + 12x13x3
------------------------------------------------------------------------------------
K – 3S = 0 + 2x3x1 + 3x4x2 + …… .. + 11x12x10 + 12x13x11
K – 3S = K – 12x13x14
Từ đó suy ra: 3S = 12x13x14
S = 4x13x14 = 728
![](https://rs.olm.vn/images/avt/0.png?1311)
Giải
Cách 1:
S = 1x2 + 2x3 + 3x4 + ……………… + 11x12 + 12x13
3S=1x2x3 + 2x3x3 + 3x4x3+ ………. + 11x12x3 + 12x13x3
Ta lấy K = 1x2x3 +2x3x4 + 3x4x5 + …… + 11x12x13 + 12x13x14
- 3S = 1x2x3 + 2x3x3 + 3x4x3+ ……… + 11x12x3 + 12x13x3
------------------------------------------------------------------------------------
K – 3S = 0 + 2x3x1 + 3x4x2 + …… .. + 11x12x10 + 12x13x11
K – 3S = K – 12x13x14
Từ đó suy ra: 3S = 12x13x14
S = 4x13x14 = 728
Cách 2:
S x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + …. + 11x12x(13-10) + 12x13x(14-11)
S x 3 = 1x2x3 + 2x3x4 – 2x3x1 + 3x4x5 – 3x4x2 + …..+ 11x12x13 – 11x12x10 +12x13x14 – 12x13x11
S x 3 = 12 x 13 x14
S = 4 x 13 x 14
S = 728
![](https://rs.olm.vn/images/avt/0.png?1311)
Nguồn: Tính tổng: 1x2 + 2x3 + 3x4 +...+ 2019x2020 + 2020x2021 - Hoc24
Đặt
![](https://rs.olm.vn/images/avt/0.png?1311)
Gọi biểu thức trên là A, ta có :
A = 1x2 + 2x3 + 3x4 + 4x5 + ...+ 99x100
A x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3
A x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98)
A x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100.
A x 3 = 99x100x101
A = 99x100x101 : 3
A = 333300
Gọi biểu thức trên là A, ta có :
A = 1x2 + 2x3 + 3x4 + 4x5 + ...+ 99x100
A x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3
A x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98)
A x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100.
A x 3 = 99x100x101
A = 99x100x101 : 3
A = 333300
![](https://rs.olm.vn/images/avt/0.png?1311)
S = 728
S = 1x2 + 2x3 + 3x4 + ……………… + 11x12 + 12x13
3S=1x2x3 + 2x3x3 + 3x4x3+ ………. + 11x12x3 + 12x13x3
Ta lấy K = 1x2x3 +2x3x4 + 3x4x5 + …… + 11x12x13 + 12x13x14
- 3S = 1x2x3 + 2x3x3 + 3x4x3+ ……… + 11x12x3 + 12x13x3
------------------------------------------------------------------------------------
K – 3S = 0 + 2x3x1 + 3x4x2 + …… .. + 11x12x10 + 12x13x11
K – 3S = K – 12x13x14
Từ đó suy ra: 3S = 12x13x14
S = 4x13x14 = 728
Cách 2:
S x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + …. + 11x12x(13-10) + 12x13x(14-11)
S x 3 = 1x2x3 + 2x3x4 – 2x3x1 + 3x4x5 – 3x4x2 + …..+ 11x12x13 – 11x12x10 +12x13x14 – 12x13x11
S x 3 = 12 x 13 x14
S = 4 x 13 x 14
S = 728
ai k minh minh k lai cho