Question

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

Answer 1

\(F=\frac{4}{2.4}+\frac{4}{4.6}+....+\frac{4}{2008.2010}\)

\(F=\frac{4}{2}.\left(\frac{1}{2.4}+\frac{1}{4.6}+....+\frac{1}{2008.2010}\right)\)

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

\(F=\frac{4}{2}.\left(\frac{1}{2}-\frac{1}{2010}\right)=\frac{4}{2}.\frac{502}{1005}=\frac{1004}{1005}\)

 

Answer 2

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

  =2(2/2.4+2/4.6+....+2/2008.2010)

=2(1/2-1/4+1/4-1/6+....+1/2008-1/2010)

=2(1/2-1/2010)

=2.\(\frac{502}{1005}\)

=\(\frac{8032}{1005}\)