Đặt A= 1.2+2.3 +.......+99.100
3A= 1.2.3+2.3.4+3.4.3 +......+ 99.100.3
3A= 1.2. (3 - 0) + 2.3.(4 - 1) +3.4. (5 - 2)....... . 99.100. (101 - 98)
3A = (1.2.3 + 2.3.4 + 3.4.5 +...... + 99.100.101) - (0.1.2 + 1.2.3 + 2.3.4 +.......+ 98.99.100)
3A = 99.100.101 - 0.1.2
3A = 999900 - 0
3A= 999900
A= 999900 : 3
A = 333300
A=1.2+2.3+3.4+…+99.100
3A = 1.2.3 + 2.3.3 + ... + 99.100.3
3A = 1.2.3 + 2.3.(4-1) + ... + 99.100.(101-98)
3A = 1.2.3 + 2.3.4 - 1.2.3 + ... + 99.100.101 - 98.99.100
3A = 99.100.101
=> A = \(\frac{99.100.101}{3}\)= 333 300
3A = 1 × 2 × 3 + 2 × 3 × ( 4 - 1 ) + ... + 99 × 100 × ( 101 - 98 )
3A = 1 × 2 × 3 + 2 × 3 × 4 - 1 × 2 × 3 + ... + 99 × 100 × 101 - 98 × 99 × 100
3A = 99 × 100 × 101 = 999900
A = 999900 ÷ 3 = 333300
Tích mình cái nha