\(S=\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{x\left(x+2\right)}=\frac{4}{9}\)
\(S=\frac{4-2}{2.4}+\frac{6-2}{4.6}+...+\frac{\left(x+2\right)-x}{x\left(x+2\right)}=\frac{4}{9}\)
\(S=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{x}-\frac{1}{x+2}=\frac{4}{9}\)
\(S=\frac{1}{2}-\frac{1}{x+2}=\frac{4}{9}\)
\(\Rightarrow\frac{1}{x+2}=\frac{1}{2}-\frac{4}{9}=\frac{1}{18}\)
\(\Rightarrow x+2=18\Rightarrow x=18-2=16\)
Vậy x=16
\(\frac{2}{2\cdot4}+\frac{2}{4\cdot6}+...+\frac{2}{x\left(x+2\right)}=\frac{4}{9}\)
\(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{x}-\frac{1}{x+2}=\frac{4}{9}\)
\(\frac{1}{2}-\frac{1}{x+2}=\frac{4}{9}\)
\(\frac{1}{x+2}=\frac{1}{2}-\frac{4}{9}\)
\(\frac{1}{x+2}=\frac{1}{18}\)
\(\Leftrightarrow x+2=18\)
=> x = 18 - 2
x = 16
Vậy x =16
