\(C=\frac{1}{11.13}+\frac{1}{13.15}+\frac{1}{15.17}+...+\frac{1}{2015.2017}\)
\(2C=\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{2015.2017}\)
\(2C=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{2015}-\frac{1}{2017}\)
\(2C=\frac{1}{11}-\frac{1}{2017}\)
\(2C=\frac{2006}{22187}\)
\(C=\frac{1003}{22187}\)
C = 1/11 . 13 + 1/13 . 15 + 1/15 . 17 + ........ + 1/2015 . 2017
C = 1/11 - 1/13 + 1/13 - 1/15 + 1/15 - 1/17 + ......... + 1/2015 - 1/2017
C = 1/11 - 1/2017
C = 2006/22187
\(C=\frac{1}{11\cdot13}+\frac{1}{13\cdot15}+\frac{1}{15\cdot17}+...+\frac{1}{2015\cdot2017}\)
\(C=\frac{1}{2}\cdot\left(\frac{2}{11\cdot13}+\frac{2}{13\cdot15}+\frac{2}{15\cdot17}+...+\frac{2}{2015\cdot2017}\right)\)
\(C=\frac{1}{2}\cdot\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17} +...+\frac{1}{2015}-\frac{1}{2017}\right)\)
\(C=\frac{1}{2}\cdot\left(\frac{1}{11}-\frac{1}{2017}\right)\)
\(C=\frac{1}{2}\cdot\frac{2006}{22187}=\frac{1003}{22187}\)
\(C=\frac{1}{11.13}+\frac{1}{13.15}+\frac{1}{15.17}+....+\frac{1}{2015.2017}\)
