Sửa đề tí :
\(S=\frac{3}{1\cdot3}+\frac{3}{3\cdot5}+\frac{3}{5\cdot7}+...+\frac{3}{2013\cdot2015}\)
\(S=\frac{3}{2}\left[\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{2013\cdot2015}\right]\)
\(S=\frac{3}{2}\left[1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2013}-\frac{1}{2015}\right]\)
\(S=\frac{3}{2}\left[1-\frac{1}{2015}\right]=\frac{3}{2}\cdot\frac{2014}{2015}=\frac{3021}{2015}\)
Ta có : S = 1/1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 +......+1/2013-1/2015
Ta gạch các phân số ở giữa còn lại 1/1 - 1/2015=2014/2015
Vậy S = 2014/2015
K 2 LẦN NHÉ
\(S=\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{2013.2015}\)
\(=\frac{3}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2013.2015}\right)\)
\(=\frac{3}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2013}-\frac{1}{2015}\right)\)
\(=\frac{3}{2}\left(1-\frac{1}{2015}\right)\)
\(=\frac{3}{2}.\frac{2014}{2015}\)
\(=\frac{3021}{2015}\)
Study well ! >_<
