Ta có:\(B=\frac{1.3}{2.2}x\frac{2.4}{3.3}x\frac{3.5}{4.4}x...x\frac{10.12}{11.11}\)

                          \(=\frac{1.2.3.4.5.6.7.8.9.10}{2.3.4.5.6.7.8.9.10.11}x\frac{3.4.5.6.7.8.9.10.11.12}{2.3.4.5.6.7.8.9.10.11}\)

                           \(=\frac{1}{11}x6\)

                             \(=\frac{6}{11}\)

             Ai thấy đúng k nha.

\(A=1+\frac{1}{3}+1+\frac{1}{8}+1+\frac{1}{15}+...+1+\frac{1}{120}=\left(1+1+...+1\right)+\left(\frac{1}{1\times3}+\frac{1}{2\times4}+\frac{1}{3\times5}+...+\frac{1}{10\times12}\right)\)\(A=10+\frac{1}{2}\times\left(\frac{2}{1\times3}+\frac{2}{2\times4}+\frac{2}{3\times5}+...+\frac{2}{10\times12}\right)=10+\frac{1}{2}\times\left(1-\frac{1}{3}+\frac{1}{2}-\frac{1}{4}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{12}\right)\)\(A=10+\frac{1}{2}\times\left(1+\frac{1}{2}+\left(-\frac{1}{3}+\frac{1}{3}\right)+\left(-\frac{1}{4}+\frac{1}{4}\right)+\left(-\frac{1}{5}+\frac{1}{5}\right)+...+\left(-\frac{1}{10}+\frac{1}{10}\right)-\frac{1}{11}-\frac{1}{12}\right)\)\(A=10+\frac{1}{2}\times\left(1+\frac{1}{2}-\frac{1}{11}-\frac{1}{12}\right)=10+\frac{175}{264}=\frac{2815}{264}\)

quy dong tich cheo len

Không quy đồng tích chéo được vì khi quy đồng tích chéo mẫu số rất lớn,không rút gọn được

`#3107.101107`

\(-16 \div (-8)+5[3-15\div5+2(-3+4)]\)

`= 2 + 5(3 - 3 - 6 + 8)`

`= 2 + 5*(-6 + 8)`

`= 2 + 5*2`

`= 2(5 + 1)`

`= 2*6 = 12`

____

`15*(-236)+15*235`

`= 15 * (-236 + 235)`

`= 15 * (-1)`

`= -15`

____

`237*(-28)+28*137`

`= 28 * (-237 + 137)`

`= 28 * (-100)`

`= -2800`

____

`(-3)*(-17)+3*(120-17)`

`= 3 * 17 + 3 * (120 - 17)`

`= 3 * (17 + 120 - 17)`

`= 3 * 120`

`= 360`

____

`(-8)*72+8*(-19)-(-8)`

`= 8 * (-72) + 8 * (-19) + 8`

`= 8 * (-72 - 19 + 1)`

`= 8 * (-90)`

`= -720`

=2x2/1x3 x 3x3/2x4x4/3x5 x ... x 11x11/10x12

=2x2x3x3x4x4x...x11x11/1x3x2x4x3x5x...x10x12

= 2x3x4x...x11)x(2x3x4x...x11)/(1x2x3x4x...x11)/(1x2x3x...x10)x(2x3x4x...x11)

=11x2/1x12

=22/12

=11/6

4/3x9/8x16/15x...x121/120=\(\dfrac{2^2}{1\cdot3}\)x\(\dfrac{3^2}{2\cdot4}\)x\(\dfrac{4^2}{3\cdot5}\)x...x\(\dfrac{11^2}{10\cdot12}\)=\(\dfrac{2}{3}\)x\(\dfrac{11}{10}\)=\(\dfrac{11}{15}\)

4/3x9/8x16/15x...x121/120=\(\dfrac{2^2}{1\cdot3}\)x\(\dfrac{3^2}{2\cdot4}\)x...x\(\dfrac{11^2}{10\cdot12}\)=\(\dfrac{2}{3}\)x\(\dfrac{11}{10}\)=\(\dfrac{11}{15}\)

\(\frac{4}{3}.\frac{9}{8}.\frac{16}{15}.\frac{25}{24}...\frac{121}{120}.\frac{144}{143}\)

\(=\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}.\frac{5.5}{4.6}...\frac{11.11}{10.12}.\frac{12.12}{11.13}\)

\(=\frac{2.2.3.3.4.4.5.5...11.11.12.12}{1.3.2.4.3.5.4.6...10.12.11.13}\)

\(=\frac{\left(2.3.4.5...11.12\right).\left(2.3.4.5...11.12\right)}{\left(1.2.3.4...10.11\right).\left(3.4.5.6...12.13\right)}\)

\(=\frac{12.2}{1.13}\)

\(=\frac{24}{13}\)

  ( Dấu \(.\)là dấu \(\times\)nha )

12 mũ 5 nhân 9 mũ 6 phần 27 mũ 5 nhân 2 mũ 12

\(\dfrac{4}{3}\cdot\dfrac{9}{8}\cdot\dfrac{16}{15}\cdot...\cdot\dfrac{400}{399}\)
\(=\dfrac{2\cdot2}{1\cdot3}\cdot\dfrac{3\cdot3}{2\cdot4}\cdot\dfrac{4\cdot4}{3\cdot5}\cdot...\cdot\dfrac{20\cdot20}{19\cdot21}\)
\(=\dfrac{2\cdot2\cdot3\cdot3\cdot4\cdot4\cdot...\cdot20\cdot20}{1\cdot3\cdot2\cdot4\cdot3\cdot5\cdot...\cdot19\cdot21}\)
\(=\dfrac{2\cdot3\cdot4\cdot...\cdot20}{1\cdot2\cdot3\cdot...\cdot19}\cdot\dfrac{2\cdot3\cdot4\cdot...\cdot20}{3\cdot4\cdot5\cdot...\cdot21}\)
\(=20\cdot\dfrac{2}{21}\)
\(=\dfrac{40}{21}\)

B=1x3/2x2x2x4/3x3x3x5/4x4x...x10x12/11x11

B=1x3x2x4x3x5x...x10x12/2x2x3x3x4x4x...x11x11

B=(1x2x3x...x10)x(2x3x5x...x12)/(2x3x4x...x11)x(2x3x4x...x11)

B=1x12/11x2

B=12/22

B=6/11

Vậy B = 6/11