\(7.\left[\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\right):2\right]\)
\(7.\left[\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right):2\right]\)
\(7.\left(\frac{1}{3}-\frac{1}{13}\right):2\)
\(7.\frac{10}{39}:2=\frac{35}{39}\)
\(\frac{7}{15}+\frac{7}{35}+\frac{7}{63}+\frac{7}{99}+\frac{7}{143}\)
\(=\frac{7}{2}\cdot\left(\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+\frac{2}{143}\right)\)
\(=\frac{7}{2}\cdot\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\right)\)
\(=\frac{7}{2}\cdot\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{7}{2}\cdot\left(\frac{1}{3}-\frac{1}{13}\right)\)
\(=\frac{7}{2}\cdot\frac{10}{39}\)
\(=\frac{35}{39}\)
