Question

\(\frac{1}{1x3}+\frac{1}{3x5}+\frac{1}{5x7}+...+\frac{1}{2013x2015}\)

      (Viết dưới dạng phân số tối giản)

Answer 1

\(=\frac{1}{1x3}+\frac{1}{3x5}+\frac{1}{5x7}+...+\frac{1}{2013x2015}\)

\(=\frac{1}{2}x\left(\frac{2}{1x3}+\frac{2}{3x5}+\frac{2}{5x7}+...+\frac{2}{2013x2015}\right)\)

\(=\frac{1}{2}x\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2013}-\frac{1}{2015}\right)\)

\(=\frac{1}{2}x\left(1-\frac{1}{2015}\right)\)

\(=\frac{1}{2}x\frac{2014}{2015}\)

\(=\frac{1007}{2015}\)

Answer 2

1/1-1/3+1/3-1/5+1/5-1/7+....+1/2013-1/2015

=1/1-1/2015

=2014/2015