Question

\(E=\frac{1}{2\cdot4}+\frac{1}{4\cdot6}+\frac{1}{6\cdot8}+....+\frac{1}{2016\cdot2018}\)

Answer 1

\(E=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+....+\frac{1}{2016.2018}\)

\(E=\frac{4-2}{2.4}+\frac{6-4}{4.6}+\frac{8-6}{6.8}+...+\frac{2018-2016}{2016.2018}\)

\(2E=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2016}-\frac{1}{2018}\)

\(E=\left(\frac{1}{2}-\frac{1}{2018}\right).\frac{1}{2}\)

\(E=\frac{504}{1009}.\frac{1}{2}\)

\(E=\frac{252}{1009}\)

Answer 2

\(E=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2016}-\frac{1}{2018}\)

\(E=\frac{1}{2}-\frac{1}{2018}\)

\(E=\frac{1005}{2018}\)

Answer 3

\(E=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2116}-\frac{1}{2018}\)

\(E=\frac{1}{2}-\frac{1}{2018}\)

\(E=\frac{1005}{2018}\)

Answer 4

\(E=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2016}-\frac{1}{2018}\)

\(E=\frac{1}{2}-\frac{1}{2018}\)

\(E=\frac{1005}{2018}\)