Question

1/1x3+1/3x5+1/5x7+...+1/2013+2015+1/2015+2016

Answer 1

phải là 1/2003.2015 chớ sao lại cộng

Answer 2

Đặt \(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2013.2015}+\frac{1}{2015.2017}\)

\(2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2013.2015}+\frac{2}{2015.2017}\)

\(2A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{2013}-\frac{1}{2015}+\frac{1}{2015}-\frac{1}{2017}\)

\(2A=1-\frac{1}{2017}\)

\(2A=\frac{2016}{2017}\)

\(A=\frac{2016}{2017}:2\)

\(A=\frac{1008}{2017}\)