\(A=\dfrac{1}{2.4}+\dfrac{1}{4.6}+...+\dfrac{1}{\left(2x-2\right).2x}=\dfrac{1}{8}\)
\(2A=\dfrac{2}{2.4}+\dfrac{2}{4.6}+...+\dfrac{2}{\left(2x-2\right).2x}=\dfrac{1}{8}.2=\dfrac{2}{8}=\dfrac{1}{4}\)
\(2A=\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{2x-2}-\dfrac{1}{2x}=\dfrac{1}{4}\)
\(2A=\dfrac{1}{2}-\dfrac{1}{2x}=\dfrac{1}{4}\)
\(A=\dfrac{1}{2}.\left(\dfrac{1}{2}-\dfrac{1}{2x}\right)=\dfrac{1}{8}\)
\(A=\dfrac{1}{2}.\dfrac{1}{2}-\dfrac{1}{2}.\dfrac{1}{2x}=\dfrac{1}{8}\)
\(A=\dfrac{1}{4}-\dfrac{1}{4x}=\dfrac{1}{8}\)
\(\Rightarrow\dfrac{1}{4x}=\dfrac{1}{4}-\dfrac{1}{8}=\dfrac{2}{8}-\dfrac{1}{8}=\dfrac{1}{8}\)
\(\Rightarrow4x=8\)
\(\Rightarrow x=8:4=2\)
