Đặt A = 1.2 + 2.3 + 3.4 + 4.5 + ... + 98.99
Suy ra 3A = 1.2.3 + 2.3.3 + 3.4.3 + 3.5.3 + ... + 98.99.3
= 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + 4.5.(6 - 3) + ... + 98.99.(100 - 97)
= 1.2.3 + 2.3.4 - 1.2.3 - 2.3.4 + 3.4.5 - 3.4.5 + 4.5.6 + ... + 98.99.100 - 97.98.99
= 98.99.100
= 970200
Suy ra A = 970200 : 3 = 323400