A=12.1.2+12.2.3+12.3.4+...+12.99.100=12(1.2+2.3+3.4+...+99.100)
Đặt B=1.2+2.3+3.4+...+99.100
⇒3B=1.2.3+2.3.3+3.4.3+...+99.100.3
⇔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⇔B=33.100.101
⇒A=12.33.100.101=166650