\(B=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{575}\)
\(=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{23.25}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{23}-\frac{1}{25}\)
\(=\frac{1}{3}-\frac{1}{25}=\frac{22}{75}\)