\(\left(\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{3001.3004}\right)\cdot\left(x+1\right)=\frac{9009}{1502}\)
\(\Leftrightarrow\frac{2}{3}\cdot\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{3001}-\frac{1}{3004}\right)\cdot\left(x+1\right)=\frac{9009}{1502}\)
\(\Leftrightarrow\frac{2}{3}\cdot\left(1-\frac{1}{3004}\right)\cdot\left(x+1\right)=\frac{9009}{1502}\)
\(\Leftrightarrow\frac{2}{3}\cdot\frac{3003}{3004}\cdot\left(x+1\right)=\frac{9009}{1502}\)
\(\Leftrightarrow\frac{1001}{1502}\cdot\left(x+1\right)=\frac{9009}{1502}\)
\(\Leftrightarrow x+1=\frac{9009}{1502}\div\frac{1001}{1502}\)
\(\Leftrightarrow x+1=9\Rightarrow x=8\)
