\(b=\frac{2}{2\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{99\times101}\)
\(b=\left(\frac{1}{3}+\frac{1}{3}\right)-\left(\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}\right)-\frac{1}{101}\)
\(b=\frac{2}{3}-\frac{1}{101}=\frac{202}{303}-\frac{3}{303}\)
\(b=\frac{199}{303}\)