Thầy ơi nhật thưởng hả thầy=))

Bài đâu em nhỉ?

\(a.\) \(A=\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}+\dfrac{1}{6\cdot7}\)

\(A=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}\)

\(A=\dfrac{1}{2}-\dfrac{1}{7}\)

\(A=\dfrac{7}{14}-\dfrac{2}{14}\)

\(A=\dfrac{5}{14}\)

\(b.\) \(D=\dfrac{2}{3\cdot4}+\dfrac{2}{4\cdot5}+...+\dfrac{2}{2022\cdot2023}\)

\(D=\dfrac{2}{3}-\dfrac{2}{4}+\dfrac{2}{4}-\dfrac{2}{5}+...+\dfrac{2}{2022}-\dfrac{2}{2023}\)

\(D=\dfrac{2}{3}-\dfrac{2}{2023}\)

\(D=\dfrac{4046}{6069}-\dfrac{6}{6069}\)

\(D=\dfrac{4040}{6969}\)

\(c.\) \(E=\dfrac{1}{1\cdot4}+\dfrac{1}{4\cdot7}+...+\dfrac{1}{37\cdot40}\)

\(E=\dfrac{1}{1}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{37}-\dfrac{1}{40}\)

\(E=\dfrac{1}{4}-\dfrac{1}{40}\)

\(E=\dfrac{10}{40}-\dfrac{1}{40}\)

\(E=\dfrac{9}{40}\)

\(d.\) \(J=\dfrac{1\cdot2\cdot3+2\cdot4\cdot6+4\cdot8\cdot12+7\cdot14\cdot21}{1\cdot3\cdot5+2\cdot6\cdot10+4\cdot12\cdot20+7\cdot21\cdot35}+\dfrac{3}{5}\)

\(J=\dfrac{1\cdot2\cdot3+1\cdot2\cdot3\cdot2\cdot2\cdot2+1\cdot2\cdot3\cdot4\cdot4\cdot4+1\cdot2\cdot3\cdot7\cdot7\cdot7}{1\cdot3\cdot5+1\cdot2\cdot5\cdot2\cdot2\cdot2+1\cdot2\cdot5\cdot4\cdot4\cdot4+1\cdot2\cdot3\cdot7\cdot7\cdot7}+\dfrac{3}{5}\)

\(J=\dfrac{1\cdot2\cdot3\cdot\left(1+2^3+4^3+7^3\right)}{1\cdot3\cdot5\cdot\left(1+2^3+4^3+7^3\right)}+\dfrac{3}{5}\)

\(J=\dfrac{1\cdot2\cdot3}{1\cdot3\cdot5}\cdot1+\dfrac{3}{5}\)

\(J=\dfrac{6}{15}+\dfrac{3}{5}\)

\(J=\dfrac{2}{5}+\dfrac{3}{5}\)

\(J=\dfrac{5}{5}=1\)

\(\dfrac{5}{9}\cdot\dfrac{7}{13}+\dfrac{5}{9}\cdot\dfrac{9}{13}-\dfrac{5}{9}:\dfrac{13}{3}\)

\(=\dfrac{5}{9}\cdot\dfrac{7}{13}+\dfrac{5}{9}\cdot\dfrac{9}{13}-\dfrac{5}{9}\cdot\dfrac{3}{13}\)

\(=\dfrac{5}{9}\cdot\left(\dfrac{7}{13}+\dfrac{9}{13}-\dfrac{3}{13}\right)\)

\(=\dfrac{5}{9}\cdot\left(\dfrac{7+9-3}{13}\right)\)

\(=\dfrac{5}{9}\cdot\dfrac{13}{13}\)

\(=\dfrac{5}{9}\cdot1=\dfrac{5}{9}\)

vâng, em camon ạ

`3/5 : (1/2 xx 3/5)`

`= 3/5 : 3/10`

`= 3/5 xx 10/3`

`= 30/15 = 2`

Tổng của `2` phân số đối nhau có giá trị là `1`.