Question

A=4/2.4+4/4.6+4/6.8+...+4/2014.2016
 

Answer 1

Ta có:

A=4/2(2/2.4+2/4.6+...+2/2014.2016)

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

A=4/2(1/2-1/2016)

A=4/2.1007/2016

=>A=1007/1008

Answer 2

\(A=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2014.2016}\)

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

\(A=2.\left(\frac{1}{2}-\frac{1}{2016}\right)\)

\(A=2.\frac{1007}{2016}\)

\(A=\frac{1007}{1008}\)