![](https://rs.olm.vn/images/avt/0.png?1311)
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt A=1.2+2.3+3.4+...+99.100
3A=1.2.3+2.3.(4-1)+3.4.(5-2)+...+99.100.(101-98)
3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100
3A=99.100.101
A=333300
![](https://rs.olm.vn/images/avt/0.png?1311)
S = 1 x 2 + 2 x 3 + ......... + 99 x 100
3S = 1 x 2 x (3-0) + 2 x 3 x (4-1) + ......+99 x 100 x (101 - 98)
3S = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + ........ + 99 x 100 x 101 - 98 x 99 x 100
3S = (1 x 2 x 3 - 1 x 2 x 3) + (2 x 3 x4 - 2 x 3 x4) +....... + (98 x 99 x 100 - 98x 99 x 100) + 99 x 100 x 101
3S = 99 x 100 x 101 = 999900
S = 999900 : 3 = 333300
Vậy S = 333300
![](https://rs.olm.vn/images/avt/0.png?1311)
=>3D =1.2.3 + 2.3.3 + 3.4.3 + ..... + 99.100 .3
=> 3D = 1.2.3 - 2.3. ( 4-1) + 3.4. (5-2) + ... + 98.99 (100 - 97 ) + 99 . 100 . ( 101-98)
=> 3D= 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 +... + 98.99.100 -97.98.99 +99.100.101-98.99.100
=> 3D= 99.100.101
=> 3D= 999 900
D= 999 900 .3 = 333 300
=>3D =1.2.3 + 2.3.3 + 3.4.3 + ..... + 99.100 .3
=> 3D = 1.2.3 - 2.3. ( 4-1) + 3.4. (5-2) + ... + 98.99 (100 - 97 ) + 99 . 100 . ( 101-98)
=> 3D= 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 +... + 98.99.100 -97.98.99 +99.100.101-98.99.100
=> 3D= 99.100.101
=> 3D= 999 900
D= 999 900 .3 = 333 300
![](https://rs.olm.vn/images/avt/0.png?1311)
Tính tổng:
1x2 + 2x3 + 3x4 + 4x5 +.............+ 99x100
Giải
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)
1/1.2+1/2.3+....+1/99.100
=1/1-1/2+1/2-1/3+...+1/99-1/100
=1/1-1/100=100/100-1/100=99/100
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt A=1.2+2.3+3.4+...+99.100
3A=1.2.3+2.3.(4-1)+3.4.(5-2)+...+99.100.(101-98)
3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100
3A=99.100.101
A=333300
S = 1.2 + 2.3 + 3.4+.....+99.100
3S=1.2.3+2.3.(4-1) + ..... + 99.100.(101-98)
3S = 1.2.3 + 2.3.4 - 1.2.3 + 99.100.101-98.99.100
3S = 99.100.101 = 999900
S = 999900 : 3 = 333300
![](https://rs.olm.vn/images/avt/0.png?1311)
S = 1x2 + 2x3 + 3x4 + 4x5 + ...+ 99x100
S x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3
S x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98)
Sx 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100.
S x 3 = 99x100x101
S= 99x100x101 : 3
S = 333300