A = 12 + 22 + 32 + ........ + 1002
= 1(2 - 1) + 2(3 - 1) + 3(4 - 1) + ........ + 100(101 - 1)
= 1.2 - 1 + 2.3 - 2 + 3.4 - 3 + ......... + 100.101 - 100
= (1.2 + 2.3 + 3.4 + ........ + 99.100) + 100.101 - (1 + 2 + 3 + ....... + 100)
= B + 10100 - \(\frac{100.101}{2}\) = B + 5050
=> A - B = 5050