Question

\(\frac{3}{30}+\frac{3}{42}+\frac{3}{56}+\frac{3}{72}+\frac{3}{90}+\frac{3}{110}+\frac{3}{132}=\frac{1}{6}X\)

Answer 1

\(\frac{3}{5.6}+\frac{3}{6.7}+......+\frac{3}{11.12}=\frac{1}{6}X\)

\(\Rightarrow3.\left(\frac{1}{5.6}+\frac{1}{6.7}+....+\frac{1}{11.12}\right)=\frac{1}{6}X\)

\(\Rightarrow3.\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+.....+\frac{1}{11}-\frac{1}{12}\right)=\frac{1}{6}X\)

\(\Rightarrow3.\left(\frac{1}{5}-\frac{1}{12}\right)=\frac{1}{6}X\)

\(\Rightarrow3.\frac{7}{60}=\frac{1}{6}X\)

\(\Rightarrow\frac{21}{60}=\frac{1}{6}X\)

\(\Rightarrow X=\frac{21}{60}\div\frac{1}{6}=\frac{21}{10}\)

Vậy \(X=\frac{21}{10}\)