Question

tinh GTBT

\(F=\frac{4}{2\cdot4}+\frac{4}{4\cdot6}+\frac{4}{6\cdot8}+...+\frac{4}{2008\cdot2010}\)

Answer 1

\(F=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)

\(F=2\left(\frac{1}{2}-\frac{1}{2010}\right)\)

\(F=2\times\frac{502}{1005}\)

\(F=\frac{1004}{1005}\)

Answer 2

F=4/2.4+4/4.6+4/6.8+..........+4/2008.2010

F=2/2-2/4+2/4-2/6+2/6-2/8+......+2/2008-2/2010

F=2/2- 2/4+2/4-2/6+2/6-2/8+......+2/2008-2/2010

F=2/2-2/2010

=>F=2008/2010=1004/1005

Answer 3

\(\text{Ta có : }\) \(F=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{1004.1005}\)

                    \(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{1004}-\frac{1}{1005}\)

                    \(=1-\frac{1}{1005}\)

                    \(=\frac{1004}{1005}\)