Question

1.2.3+2.3.4+3.4.5+..+99.100.101

Answer 1

Đặt \(A=1.2.3+2.3.4+3.4.5+...+99.100.101\)

\(\Rightarrow4A=1.2.3.4+2.3.4.4+...+99.100.101.4\)

\(=1.2.3\left(4-0\right)+2.3.4\left(5-1\right)+...+99.100.101\left(102-98\right)\)

\(=\left(1.2.3.4+2.3.4.5+...+99.100+101.102\right)-\left(0.1.2.3+1.2.3.4+...+98.99.100.101\right)\)

\(=99.100.101.102-0.1.2.3\)

\(=101989800\)

\(\Rightarrow A=101989800:4=25497450\)

Vậy \(A=25497450.\)