Tính tổng : A=1.2+2.3+3.4+..+19.20 

               3A = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ..... + 19.20.21

               3A = 19.20.21

                A = \(\frac{19.20.21}{3}=3990\)

Tính tổng : A=1.2+2.3+3.4+..+19.20

3a=1.2.3-1.2.3.+2.3.4-2.3.4+......+19.20.21

3a=19.20.21

a=19.20.21:3=3990

L-iek giùm tôi vs bn oi

2660 bạn nhé

\(M=1\cdot2+2\cdot3+3\cdot4+...+19\cdot20=\)

\(3\times M=1\cdot2\cdot3+2\cdot3\cdot3+....+19\cdot20\cdot3=\)

\(3\times M=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+....+19\cdot20\cdot\left(21-18\right)=\)

\(3\times M=1\cdot2\cdot3+2\cdot3\cdot4+...+19\cdot20\cdot21-1\cdot2\cdot3-...-18\cdot19\cdot20=\)

\(3\times M=19\cdot20\cdot21\)

\(M=\frac{19\cdot20\cdot21}{3}\)

\(M=2660\)

  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

1230

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^_^

D=1.2+2.3+3.4+...+19.20

=>3D=1.2.3+2.3.3+3.4.3+...+19.20

=1.2.3+2.3(4-1)+3.4(5-2)+...+19.20(21-18)

=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+19.20.21-18.19.20

=>3D=1.2.3+2.3.3+3.4.3+...+19.20

=1.2.3+2.3(4-1)+3.4(5-2)+...+19.20(21-18)

=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+19.20.21-18.19.20

=19.20.21=7980

=>D=7980:3=2660

Vậy D=2660

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

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

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

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

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

2.(1/1.2+1/2.3+.....+1/18.19+1/19.20)

2.(1/1-1/2+1/2-1/3+......+1/19-1/20)

2.(1/1-1/20)= 2.19/20=19/10

Mỏi tay nhắm . không viết đầu bài đâu >.<

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

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

= \(2\left(1-\frac{1}{20}\right)\)

= \(2.\frac{19}{20}\)

= \(\frac{19}{10}\)

Mị không chắc đâu :3

\(\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{19\cdot20}\right)\div x=\frac{9}{10}\)

\(\Leftrightarrow\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{19}-\frac{1}{20}\right)\div x=\frac{9}{10}\)

\(\Leftrightarrow\left(\frac{1}{1}-\frac{1}{20}\right)\div x=\frac{9}{10}\)

\(\Leftrightarrow\frac{19}{20}\div x=\frac{9}{10}\)

\(\Leftrightarrow x=\frac{19}{18}\)

Sửa đề : \(\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{19.20}\right):x=\frac{9}{10}\)

\(\Leftrightarrow VT=\frac{9}{10}x\)

\(\Leftrightarrow\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{19}-\frac{1}{20}\right)=\frac{9}{10}x\)

\(\Leftrightarrow\left(1-\frac{1}{20}\right)=\frac{9}{10}x\Leftrightarrow\frac{19}{20}=\frac{9}{10}x\)

\(\Leftrightarrow\frac{19}{20}=\frac{18x}{20}\) Khử mẫu ta đc : \(\Leftrightarrow18x=19\Leftrightarrow x=\frac{19}{18}\)

Ta có:

S=1.2+2.3+3.4+...+19.20

3S=1.2.3+2.3.(4-1)+...+19.20.(21-18)

3S=1.2.3+2.3.4-2.3.1+...+19.20.21-18.19.20

3S=19.20.21=> S=\(\frac{19.20.21}{3}\)= 2660.

S = 1.2 + 2.3 + ... + 19.20

3S = 1.2.(3 - 0) + 2.3.(4 - 1) +...+ 19.20.(21 - 18)

3S = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 +...+ 19.20.21 - 18.19.20

3S = (1.2.3 + 2.3.4 +...+ 19.20.21) - (0.1.2 + 1.2.3 +...+ 18.19.20)

3S = 19.20.21 - 0.1.2

3S = 19.20.21

S = \(\frac{19.20.21}{3}\)

S = 2660

A x 3 = 1.2.3 + 2.3.3 + ...+ 19.20.3

A x 3 = 1.2.( 3 - 1) + 2.3.(4 - 1) + ...+ 19.20.( 21-18)

A x 3 = ( 1.2.3 + 2.3.4 + ....+ 19.20.21) - ( 0.1.2 + 1.2.3 + ....+ 18.19.20)

=> A x 3 =  19 x 20 x 21 = 7890 

\(3A=1.2.3+2.3.3+....+19.20.3\)

\(3A=1.2.\left(3-0\right)+2.3.\left(4-1\right)+....+19.20\left(21-18\right)\)

\(3A=1.2.3-1.2.0+2.3.4-2.3.1+....+19.20.21-19.20.18\)

ta có thể thấy 1.2.3 = 2.3.1 và những con số khác cũng vậy

\(\Rightarrow3A=19.20.21\)

mink nghĩ vậy bạn ạ, sai đừng trách mink nha