Question

1phần 3*5 + 1 phần 5 * 7 +1 phần 7 * 9 +1 phần 9 * 11 +  1 phần 11 *13 ? 

Answer 1

\(=\frac{1}{2}\left(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{11\cdot13}\right)=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\right)\)

\(=\frac{1}{2}\left[\left(\frac{1}{3}-\frac{1}{13}\right)+\left(\frac{1}{5}-\frac{1}{5}\right)+...+\left(\frac{1}{11}-\frac{1}{11}\right)\right]=\frac{1}{2}\left[\left(\frac{13}{39}-\frac{3}{39}\right)+0+...+0\right]\)

\(=\frac{1}{2}\cdot\frac{10}{39}=\frac{5}{39}\)