\(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{97.99}\)
\(=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{97}-\frac{1}{99}\)
\(=\frac{1}{11}-\frac{1}{99}\)
\(=\frac{9}{99}-\frac{1}{99}=\frac{8}{99}\)
2/11.13 + 2/13.15 + 2/15.17 +.....+2/97.99
=2/2 .( 2/11 - 2/13 + 2/13 - 2/15 + 2/15 - 2/17 +.....+2/97 - 2/99
=2/2.(1/11 - 1/13 +1/13 -1/15 + 1/15 - 1/17 +......+ 1/97 - 1/99
=1.(1/11 - 1/99)
=1. 8/99
=8/99
\(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{97.99}\)
=\(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{97}-\frac{1}{99}\)
=\(\frac{1}{11}-\frac{1}{99}\)
=\(\frac{8}{99}\)