\(S=\frac{3}{2}\left(\frac{2}{5.7}+\frac{2}{7.9}+....+\frac{2}{99.101}\right)=\frac{3}{2}\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-...-\frac{1}{101}\right)=\frac{3}{2}\left(\frac{1}{5}-\frac{1}{101}\right)\)
\(=\frac{3}{2}.\frac{96}{505}=\frac{288}{1010}\)
\(S=\frac{3}{5.7}+\frac{3}{7.9}+\frac{3}{9.11}+...+\frac{3}{99.101}\)
\(\Rightarrow S=\frac{3}{2}\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{99.101}\right)\)
\(\Rightarrow S=\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{99}-\frac{1}{101}\right)\)
\(\Rightarrow S=\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{101}\right)=\frac{3}{2}.\frac{96}{505}\)
\(\Rightarrow S=\frac{144}{505}\)
S = \(\frac{3}{5\times7}+\frac{3}{7\times9}+\frac{3}{9\times11}+..+\frac{3}{99\times101}\)
=\(\frac{3}{5}-\frac{3}{7}+\frac{3}{7}-\frac{3}{9}+...+\frac{3}{99}-\frac{3}{101}\)(Công thức là thế !)
=\(\frac{3}{5}-\frac{3}{101}\)
=\(3\times\left(\frac{1}{5}-\frac{1}{101}\right)\)
=3\(\times\frac{96}{505}\)
=\(\frac{288}{505}\)
