Ta có: A = 1 . 4 + 2 . 5 + 3 . 6 + ... + 99 . 102
= 1 . (2 + 2) + 2 . (3 + 2) + 3 . (4 + 2) + ... + 99 . (100 + 2)
= (1 . 2 + 1 . 2) + (2 . 3 + 2 . 2) + (3 . 4 + 3 . 2) + ... + (99 . 100 + 99 . 2)
= (1 . 2 + 2 . 3 + 3 . 4 + ... + 99 . 100) + (1 . 2 + 2 . 2 + 3 . 2 + ... + 99 . 2)
Đặt B = 1 . 2 + 2 . 3 + 3 . 4 + ... + 99 . 100
3B = 1 . 2 . 3 + 2 . 3 . (4 - 1) + 3 . 4 . (5 - 2) + ... + 99 . 100 . (101 - 98)
3B = 1 . 2 . 3 + 2 . 3 . 4 - 1 . 2 . 3 + 3 . 4 . 5 - 2 . 3 . 4 + ... + 99 . 100 . 101 - 98 . 99 . 100
3B = 99 . 100 . 101
3B = 999900
B = 333300
Thay vào A ta có: A = 333300 + (1 . 2 + 2 . 2 + 3 . 2 + ... + 99 . 2) = 333300 + (1 + 2 + 3 + ... + 99) . 2 = 333300 + 99 . 100 : 2 . 2 = 333300 + 99 . 100 = 333300 + 9900 = 343200
A=1.(2+2)+2.(3+2)+3.(4+2)+.........+99.(100+2)
A=(1.2+1.2)+(2.3+2.2)+(3.4+3.2)+..............+(99.100+99.2)
A=1.2+2.3+3.4+........+99.100+1.2+2.2+3.2+4.2+.......+99.2
Đặt B=1.2+2.3+.........+99.100
3B=1.2.(3-0)+2.3.(4-1)+............+99.100.(101-98)
3B=1.2.3+2.3.4+.............+99.100.101-0.1.2-1.2.3-........-98.99.100
3B=99.100.101
3B=999900
B=333300
A=333300+(1+2+...........+99).2
A=333300+100.99:2.2
A=333300+100.99
A=333300+9900
A=343200
A=1.(2+2)+2.(3+2)+3.(4+2+...+99.(100+2)
A(1.2+1.2)+(2.3+2.2)+(3.4+3.2)+...+(99.100+99.2)
A=1.2+2.3+3.4+...+99.100+1.2+2.3+3.2+4.2+99.2
Dat B=1.2+2.3+...+99.100
3B=1.2.(3-0)+2.3+(4-1)+...+99.100.(101-98)
3B=1.2.3+2.3.4+...+99.1000.101-0.1.2-1.2.3-...-98.99.100
3b=99.100.101
3b=999900
B=999900:3=333300
A=333300+(1+2+...+99).2
A=333300+100.99:2.2
A=333300+100.99
A=333300+9900
A=343200