\(M=1\cdot2+2\cdot3+3\cdot4+...+19\cdot20=\)
\(3\times M=1\cdot2\cdot3+2\cdot3\cdot3+....+19\cdot20\cdot3=\)
\(3\times M=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+....+19\cdot20\cdot\left(21-18\right)=\)
\(3\times M=1\cdot2\cdot3+2\cdot3\cdot4+...+19\cdot20\cdot21-1\cdot2\cdot3-...-18\cdot19\cdot20=\)
\(3\times M=19\cdot20\cdot21\)
\(M=\frac{19\cdot20\cdot21}{3}\)
\(M=2660\)
M = 1.2+2.3+3.4+...+19.20
3M= 1.2.3+2.3.3+3.4.3+...+19.20.3
3M=1.2(3-0)+2.3(4-1)+3.4(5-2)+...+19.20(21-18)
3M=0.1.2-1.2.3+1.2.3-2.3.4+2.3.4-3.4.5+...+18.19.20-19.20.21
3M=19.20.21
3M=7980
M=2660
