\(A=1.2+2.3+....+99.100\)
\(\Rightarrow3A=1.2.\left(3-0\right)+2.3.\left(4-1\right)+....+99.100.\left(101-98\right)\)
\(\Rightarrow3A=1.2.3-0.1.2+2.3.4-1.2.3+.....+99.100.101-98.99.100\)
\(\Rightarrow3A=99.100.101\)
\(\Rightarrow A=\frac{99.100.101}{3}\)
=> A = 33330