A = 1.2 + 2.3 + 3.4 + 4.5 + ...+ 99.100
3A =3.(1.2 + 2.3 + 3.4 + 4.5 + ...+ 99.100)
=1.2.3 + 2.3.3 + 3.4.3 + 4.5.3 + ... + 99.100.3
= 1.2.3 + 2.3. (4-1) + 3.4. (5-2) + 4.5. (6-3) + ... + 99.100. (101-98)
= 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + 4.5.6 - 3.4.5 + ... + 99.100.101 - 98.99.100
= 99x100x101
⇒A = 99.100.101 : 3
⇒A = 333300
Vậy A = 333300