\(S=\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}+..............+\frac{2}{93\cdot95}\)
\(=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+............+\frac{1}{93}-\frac{1}{95}\)
\(=\frac{1}{5}-\frac{1}{95}\)
S = 2/5.7+ 2/7.9+...+2/93.95
=1/5-1/7+1/7-1/9+1/11+...+1/93+1/95
=1/5-1/95
=19/95-1/95
=18/95