\(=\dfrac{1}{3}\left(1\times2\times3+2\times3\times3+...+19\times20\times3\right)\\ =\dfrac{1}{3}\left[1\times2\times\left(3-0\right)+2\times3\times\left(4-1\right)+...+19\times20\times\left(21-18\right)\right]\\ =\dfrac{1}{3}\left(1\times2\times3-1\times2\times3+2\times3\times4-...-18\times19\times20+19\times20\times21\right)\\ =\dfrac{1}{3}\times19\times20\times21=2660\)

Đặt \(A=\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+....+\frac{2}{18.19}+\frac{2}{19.20}\)

\(A=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\right)\)

\(A=2\left(1-\frac{1}{20}\right)\)

\(A=2.\frac{19}{20}=\frac{19}{10}\)

\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{18.19}+\frac{2}{19.20}\)

\(=2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{18.19}+\frac{1}{19.20}\right)\)

\(=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\right)\)

\(=2\left(1-\frac{1}{20}\right)\)

\(=2.\frac{19}{20}\)

\(=\frac{19}{10}\)

Ta có : \(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+......+\frac{2}{19.20}\)

\(=2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{19.20}\right)\)

\(=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+......+\frac{1}{19}-\frac{1}{20}\right)\)

\(=2\left(1-\frac{1}{20}\right)=2.\frac{19}{20}=\frac{19}{10}\)

A = \(\frac{1}{1\times2}\) + \(\frac{1}{2\times3}\) + \(\frac{1}{3\times4}\) + ... + \(\frac{1}{19\times20}\) + \(\frac{1}{20\times21}\)

A = \(\frac11\) - \(\frac12\) + \(\frac12\) - \(\frac13\) + \(\frac13\) - \(\frac14\) + ... + \(\frac{1}{19}\) - \(\frac{1}{20}\) + \(\frac{1}{20}\) - \(\frac{1}{21}\)

A = \(\frac11\) - \(\frac{1}{21}\)

A = \(\frac{20}{21}\)

Ta có: \(\frac{1}{1\times2}+\frac{1}{2\times3}+\cdots+\frac{1}{20\times21}\)

\(=1-\frac12+\frac12-\frac13+\cdots+\frac{1}{20}-\frac{1}{21}\)

\(=1-\frac{1}{21}=\frac{20}{21}\)

\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\ldots+\frac{1}{19\times20}+\frac{1}{20\times21}\)

\(=\frac11-\frac12+\frac12-\frac13+\frac14-\frac14+\ldots+\frac{1}{20}-\frac{1}{21}\)

\(=1-\frac{1}{21}\)

Vậy kết quả của phép tính trên là \(=\frac{20}{21}\)

lam ơn trả lời câu này

\(\dfrac{2}{1\cdot2}+\dfrac{2}{2\cdot3}+\dfrac{2}{3\cdot4}+...+\dfrac{2}{19\cdot20}\)

\(=2\cdot\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{19}-\dfrac{1}{20}\right)\)

\(=2\cdot\left(1-\dfrac{1}{20}\right)\)

\(=2\cdot\dfrac{19}{20}\)

\(=\dfrac{19}{10}\)

\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{18.19}+\frac{2}{19.20}\)

\(=2.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{18.19}+\frac{1}{19.20}\right)\)

\(=2.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\right)\)

\(=2.\left(1-\frac{1}{20}\right)\)

\(=2.\frac{19}{20}=\frac{19}{10}\)

A=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+....+1/19-1/20

A=1-1/20

A=20/20-1/20

A=19/20

19/20 nha ban 

             tich nha

19/20! Nhớ trả lời lại các câu hỏi của mình nhé, buồn quá rồi.

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{18.19}+\frac{1}{19.20}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\)

\(=1-\frac{1}{20}=\frac{19}{20}\)

Vậy\(A=\frac{19}{20}\)