Ta có : \(\frac{1}{2}+\frac{1}{14}+\frac{1}{35}+...+\frac{1}{x\left(x+3\right):2}=\frac{9}{14}\)
\(\Rightarrow2\left(\frac{1}{4}+\frac{1}{28}+\frac{1}{70}+...+\frac{1}{x\left(x+3\right)}\right)=\frac{9}{14}\)
\(\Rightarrow2.\frac{1}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{x\left(x+3\right)}\right)=\frac{9}{14}\)
\(\Rightarrow\frac{2}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{x}-\frac{1}{x+3}\right)=\frac{9}{14}\)
\(\Rightarrow1-\frac{1}{x+3}=\frac{27}{28}\)
\(\Rightarrow\frac{1}{x+3}=\frac{1}{28}\)
=> x + 3 = 28
=> x = 25