2870 ĐÚNG NHÉ BẠN !
\(C=1x\left(2-1\right)+2x\left(3-1\right)+3x\left(4-1\right)+...+20x\left(21-1\right)\)
\(=1x2-1+2x3-2+3x4-3+...+20x21-20\)
\(=\left(1x2+2x3+3x4+...+20x21\right)-\left(1+2+3+...+20\right)\)
\(A=1x2+2x3+3x4+...+21x21\)
\(3xA=1x2x3+2x3x3+3x4x3+...+20x21x3\)
\(3xA=1x2x3+2x3x\left(4-1\right)+3x4x\left(5-2\right)+...+20x21x\left(22-19\right)\)
\(3xA=1x2x3-1x2x3+2x3x4-2x3x4+3x4x5-...-19x20x21+20x21x22\)
\(3xA=20x21x22\Rightarrow A=20x7x22=3080\)
\(B=1+2+3+...+20=\frac{20x\left(1+20\right)}{2}=210\)
\(C=A-B=3080-210=2870\)
Bài làm:
\(1+2.2+3.3+...+20.20\)
\(=1.\left(2-1\right)+2\left(3-1\right)+3\left(4-1\right)+...+20\left(21-1\right)\)
\(=1.2-1+2.3-2+3.4-3+...+20.21-20\)
\(=\left(1.2+2.3+3.4+...+20.21\right)-\left(1+2+3+...+20\right)\)
\(=\frac{1}{3}\left(1.2.3+2.3.3+...+20.21.3\right)-\frac{\left(20+1\right).20}{2}\)
\(=\frac{1}{3}\left[1.2.3+2.3.\left(4-1\right)+...+20.21.\left(22-19\right)\right]-210\)
\(=\frac{1}{3}\left(1.2.3-1.2.3+2.3.4-...-19.20.21+20.21.22\right)-210\)
\(=\frac{1}{3}.20.21.22-210\)
\(=3080-210\)
\(=2870\)
Học tốt!!!!
