\(A=2\left(1.30+2.29+3.28+...+15.16\right)=\)
\(=2.\left[1.30+2.\left(30-1\right)+3.\left(30-2\right)+...+15.\left(30-14\right)\right]=\)
\(=2.\left(1.30-1.2+2.30+3.30-2.3+4.30-3.4+...+15.30-14.15\right)=\)
\(=2.\left[30.\left(1+2+3+...+15\right)-\left(1.2+2.3+3.4+...+14.15\right)\right]=\)
Đặt \(B=1+2+3+...+15=\frac{15.\left(1+15\right)}{2}=120\)
Đặt \(C=1.2+2.3+3.4+...+14.15\)
\(\Rightarrow3C=1.2.3+2.3.3+3.4.3+...+14.15.3=\)
\(=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+14.15.\left(16-13\right)=\)
\(=1.2.3-1.2.3+2.3.4-2.3.4+3.4.5-...-13.14.15+14.15.16=14.15.16\)
\(\Rightarrow C=\frac{14.15.16}{3}=5.14.16=1120\)
\(\Rightarrow A=2.\left(30.B-C\right)=2\left(30.120-1120\right)=4960\)
