Question

[Mitt]

Giúp với ạ!!! E cảm ơn!!!

Answer 1

[Nguyễn Vũ Minh Hiếu]

Ta có :

\(A=\frac{\frac{3}{7}-\frac{3}{17}+\frac{3}{37}}{\frac{5}{7}-\frac{5}{17}+\frac{5}{37}}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}}{\frac{7}{2}-\frac{7}{3}+\frac{7}{4}-\frac{7}{5}}\)

\(\Rightarrow A=\frac{3\left(\frac{1}{7}-\frac{1}{17}+\frac{1}{37}\right)}{5\left(\frac{1}{7}-\frac{1}{17}+\frac{1}{37}\right)}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}}{7\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}\right)}\)

\(\Rightarrow A=\frac{3}{5}+\frac{1}{7}=\frac{21}{35}+\frac{5}{35}=\frac{26}{35}\)

Answer 2

[Xyz OLM]

b) Ta có \(\frac{7}{3.6}+\frac{7}{6.9}+\frac{7}{9.12}+...+\frac{7}{66.69}=\frac{7}{3}.\left(\frac{3}{3.6}+\frac{3}{6.9}+\frac{3}{9.12}+...+\frac{3}{66.69}\right)\)

\(=\frac{7}{3}\left(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+...+\frac{1}{66}-\frac{1}{69}\right)\)

\(=\frac{7}{3}\left(\frac{1}{3}-\frac{1}{69}\right)=\frac{7}{3}.\frac{22}{69}=\frac{154}{207}\)

Lại có \(\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{67.69}=\frac{5}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{67.69}\right)\)

\(=\frac{5}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{67}-\frac{1}{69}\right)\)

\(=\frac{5}{2}\left(1-\frac{1}{69}\right)=\frac{5}{2}.\frac{68}{69}=\frac{170}{69}\)

Khi đó B = \(\frac{154}{207}:\frac{170}{69}=\frac{154.69}{207.170}=\frac{77}{255}\)