\(A=1.2+2.3+3.4+...+99.100\)
\(3A=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+99.100.\left(101-98\right)\)
\(3A=99.100.101\)
\(A=33.100.101=333300\)
\(B=1^2+2^2+3^2+...+199^2\)
\(=1.2-1+2.3-2+3.4-3+...+199.200-199\)
\(=\left(1.2+2.3+3.4+...+199.200\right)-\left(1+2+3+...+199\right)\)
\(=\frac{199.200.201}{3}-\frac{\left(1+199\right).199}{2}\)
\(=2666600-19900=2646700\)