Question

\(\frac{1}{2x4}\)+\(\frac{1}{4x6}\)+\(\frac{1}{6x8}\)+......+\(\frac{1}{2014x2016}\)

Answer 1

Đặt A =\(\frac{1}{2x4}+\frac{1}{4x6}+\frac{1}{6x8}+...+\frac{1}{2014x2016}\)

A x 2 = \(\frac{2}{2x4}+\frac{2}{4x6}+\frac{2}{6x8}+...+\frac{2}{2014x2016}\)

A x 2 = \(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2014}-\frac{1}{2016}\)

A x 2 = \(\frac{1}{2}-\frac{1}{2016}=\frac{1007}{2016}\)

A = \(\frac{1007}{2016}:2=\frac{1007}{4032}\)

          Đáp số: \(\frac{1007}{4032}\)

Answer 2

Gọi tông trên là A 

2A=2/2.4+2/4.6+2/6.8+........+2/2014.2016

2A=1/2-1/4+1/4-1/6+.........+1/2014-1/2016

2A=1/2-(1/4-1/4)+(1/6-1/6)+...........+(1/2014-1/2014)-1/2016

2A=1/2-1/2016

2A=1007/2016

A=1007/4032

Answer 3

                 Đặt \(A=\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{2014.2016}\)

                   \(2A=\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{2014.2016}\)

                   \(2A=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2014}-\frac{1}{2016}\)

                  \(2A=1-\frac{1}{2016}=\frac{2015}{2016}\)

                  \(A=\frac{2015}{2016}:2=\frac{2015}{4032}\)

               Ủng hộ mk nha !!! ^_^