Question

[Nguyễn Trung Hiếu]

Tìm

Answer 1

[Nguyễn Lương Bảo Tiên]

\(A=\frac{5}{6}+\frac{5}{12}+\frac{5}{20}+\frac{5}{30}+\frac{5}{42}\)

\(A=5\cdot\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}\right)\)

\(A=5\cdot\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)

\(A=5\cdot\left(\frac{1}{2}-\frac{1}{7}\right)\)

\(A=5\cdot\frac{5}{14}\)

\(A=\frac{25}{14}\)

dấu chấm là dấu nhân

Answer 2

[Minh Triều]

\(A=\frac{5}{6}+\frac{5}{12}+\frac{5}{20}+\frac{5}{30}+\frac{5}{42}\)

\(=5\times\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)\)

\(=5\times\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)\)

\(=5\times\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)

\(=5\times\left(\frac{1}{2}-\frac{1}{7}\right)=5\times\left(\frac{7}{14}-\frac{2}{14}\right)=5\times\frac{5}{14}\)

\(=\frac{25}{14}\)