Sửa đề

\(\dfrac{2}{1^2}\cdot\dfrac{6}{2^2}\cdot\dfrac{12}{3^3}\cdot.......\cdot\dfrac{110}{10^2}\cdot x=-20\)

\(\dfrac{2}{1\cdot1}\cdot\dfrac{2\cdot3}{2\cdot2}\cdot\cdot\cdot\cdot\dfrac{11\cdot10}{10\cdot10}\cdot x=-20\)

\(\dfrac{\left(2\cdot3\cdot4\cdot....\cdot11\right)}{\left(1\cdot2\cdot3\cdot4\cdot...\cdot10\right)}\cdot\dfrac{\left(1\cdot2\cdot3\cdot4\cdot5\cdot...\cdot10\right)}{\left(1\cdot2\cdot3\cdot4\cdot...\cdot10\right)}\cdot x=-20\)

\(11\cdot x=-20\\ x=-\dfrac{20}{11}\)

Ko đề cho thêm \(\dfrac{20}{4²}\) mà 

Câu 1:
\(B=\dfrac{5}{2.1}+\dfrac{4}{1.11}+\dfrac{3}{11.2}+\dfrac{1}{2.15}+\dfrac{13}{15.4}\)

\(\Rightarrow B=\dfrac{1}{7}\left(\dfrac{5}{2.7}+\dfrac{4}{7.11}+\dfrac{3}{11.14}+\dfrac{1}{14.15}+\dfrac{1}{15.28}\right)\)

\(\Rightarrow B=\dfrac{1}{7}\left(\dfrac{1}{2}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{15}+\dfrac{1}{15}-\dfrac{1}{28}\right)\)

\(\Rightarrow B=\dfrac{1}{7}\left(\dfrac{1}{2}-\dfrac{1}{28}\right)\)

\(\Rightarrow B=\dfrac{1}{7}.\dfrac{13}{28}\)

\(\Rightarrow B=\dfrac{13}{196}\)

Vậy \(B=\dfrac{13}{196}\)

Câu 2:

\(D=\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{20}}\)

\(\Rightarrow2D=1+\dfrac{1}{2}+...+\dfrac{1}{2^{19}}\)

\(\Rightarrow2D-D=\left(1+\dfrac{1}{2}+...+\dfrac{1}{2^{19}}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{20}}\right)\)

\(\Rightarrow D=1-\dfrac{1}{2^{20}}< 1\)

\(\Rightarrow D< 1\left(đpcm\right)\)

Vậy...

\(\left(0.25\right)^{10}.4^{10}+\sqrt{5^2-3^2}\)
\(=0.4^{10}+\sqrt{25-9}\)
\(=0+\sqrt{16}=0+4=4\)

\(\dfrac{5}{20}+\dfrac{18}{11}-25\%-\left(\dfrac{18}{11}-\dfrac{4}{9}\right)\)
\(=\dfrac{5}{20}+\dfrac{18}{11}-\dfrac{1}{4}-\dfrac{18}{11}+\dfrac{4}{9}\)
\(=\left(\dfrac{5}{20}-\dfrac{1}{4}\right)+\left(\dfrac{18}{11}-\dfrac{18}{11}\right)+\dfrac{4}{9}\)
\(=0+0+\dfrac{4}{9}=\dfrac{4}{9}\)

    (0,25)¹⁰.4¹⁰ + \(\sqrt{5^2-3^2}\)

=   (0,25 .4)¹⁰ + \(\sqrt{25-9}\)

= 1¹⁰ + \(\sqrt{16}\)

= 1 + 4 

= 5

\(\dfrac{5}{20}\) + \(\dfrac{18}{11}\) - 25% - ( \(\dfrac{18}{11}\) - \(\dfrac{4}{9}\))

= 25% +  \(\dfrac{18}{11}\) - 25% - \(\dfrac{18}{11}\) + \(\dfrac{4}{9}\)

= ( 25% - 25%)  + ( \(\dfrac{18}{11}\) - \(\dfrac{18}{11}\)) + \(\dfrac{4}{9}\)

= 0  + 0 + \(\dfrac{4}{9}\)

= \(\dfrac{4}{9}\)

\(A=\dfrac{4}{1\cdot2}+\dfrac{4}{2\cdot3}+\dfrac{4}{3\cdot4}+...+\dfrac{4}{2022\cdot2023}\\ A=4\cdot\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{2022\cdot2023}\right)\\ A=4\cdot\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2022}-\dfrac{1}{2023}\right)\\ A=4\cdot\left(\dfrac{1}{1}-\dfrac{1}{2023}\right)\\ A=4\cdot\dfrac{2022}{2023}\\ A=\dfrac{8088}{2023}\)

giúp mình nhé! ngày mai mình kiểm tra đề cương r.

`A = 4/(1.2) + 4/(2.3) + ....+ 4/(2022.2023)`

`= 4 . (1/(1.2) + 1/(2.3) + ....+ 1/(2022.2023))`

`= 4 . (1 - 1/2 + 1/2 - 1/3 +.....+ 1/2022 - 1/2023)`

`= 4 . (1 - 1/2023)`

`= 4 . 2022/2023`

`= 8088/2023`

\(B=5\dfrac{9}{10}:\dfrac{3}{2}-\left(2\dfrac{1}{3}.4\dfrac{1}{2}-2.2\dfrac{1}{3}\right):\dfrac{7}{4}\)

\(B=\dfrac{59}{10}:\dfrac{3}{2}-\left(\dfrac{7}{3}.\dfrac{9}{2}-2.\dfrac{7}{3}\right):\dfrac{7}{4}\)

\(B=\dfrac{59}{10}:\dfrac{3}{2}-\left(\dfrac{63}{6}-\dfrac{14}{3}\right):\dfrac{7}{4}\)

\(B=\dfrac{59}{10}:\dfrac{3}{2}-\left(\dfrac{63}{6}-\dfrac{28}{6}\right):\dfrac{7}{4}\)

\(B=\dfrac{59}{10}:\dfrac{3}{2}-\dfrac{35}{6}:\dfrac{7}{4}\)

\(B=\dfrac{59}{10}.\dfrac{2}{3}-\dfrac{35}{6}.\dfrac{4}{7}\)

\(B=\dfrac{59}{15}-\dfrac{10}{3}\)

\(B=\dfrac{59}{15}-\dfrac{50}{15}\)

\(B=\dfrac{3}{5}\)

B=\(5\dfrac{9}{10}:\dfrac{3}{2}-\left(2\dfrac{1}{3}.4\dfrac{1}{2}-2.2\dfrac{1}{3}\right):\dfrac{7}{4}\)

B=\(\dfrac{59}{10}:\dfrac{3}{2}-\left(\dfrac{7}{3}.\dfrac{9}{2}-2.\dfrac{7}{3}\right):\dfrac{7}{4}\)

B=\(\dfrac{59}{15}-\left(\dfrac{21}{2}-\dfrac{14}{3}\right):\dfrac{7}{4}=\dfrac{59}{15}-\left(\dfrac{63-28}{6}\right):\dfrac{7}{4}\)

B=\(\dfrac{59}{15}-\dfrac{35}{6}:\dfrac{7}{4}\)

B=\(\dfrac{59}{15}-\dfrac{10}{3}=\dfrac{59-50}{15}\)

B=\(\dfrac{3}{5}\)

\(B=\dfrac{2}{1.2.3}+\dfrac{2}{2.3.4}+\dfrac{2}{3.4.5}+\dfrac{2}{4.5.6}+\dfrac{2}{5.6.7}+\dfrac{2}{6.7.8}\)

\(=\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+...+\dfrac{1}{6.7}-\dfrac{1}{7.8}\)

\(=\dfrac{1}{1.2}-\dfrac{1}{7.8}\)

\(=\dfrac{1}{2}-\dfrac{1}{56}=\dfrac{27}{56}\)

3/ \(2\left(x-3\right)-3\left(1-2x\right)=4+4\left(1-x\right)\)

\(\Leftrightarrow2x-6-3+6x=4+4-4x\)

\(\Leftrightarrow8x-9=8-4x\)

\(\Leftrightarrow8x+4x=8+9\)

\(\Leftrightarrow12x=17\)

\(\Leftrightarrow x=\dfrac{17}{12}\)

Vậy \(x=\dfrac{17}{12}\)

4/ \(\dfrac{x-2}{2}-\dfrac{1+x}{3}=\dfrac{4-3x}{4}-1\)

\(\Leftrightarrow6\left(x-2\right)-4\left(1+x\right)=3\left(4-3x\right)-12\)

\(\Leftrightarrow6x-12-4-4x=12-9x-12\)

\(\Leftrightarrow6x-4-4x=12-9x\)

\(\Leftrightarrow2x-4=12-9x\)

\(\Leftrightarrow2x+9x=12+4\)

\(\Leftrightarrow11x=16\)

\(\Leftrightarrow x=\dfrac{16}{11}\)

Vậy \(x=\dfrac{16}{11}\)