\(\frac{4}{2\cdot4}+\frac{4}{4\cdot6}+...+\frac{4}{2008\cdot2010}+x=-\frac{1}{1005}\)
\(2\cdot\left(\frac{2}{2\cdot4}+\frac{2}{4\cdot6}+...+\frac{2}{2008\cdot2010}\right)+x=-\frac{1}{1005}\)
\(2\cdot\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2008}-\frac{1}{2010}\right)+x=-\frac{1}{1005}\)
\(2\cdot\left[\left(\frac{1}{2}-\frac{1}{2010}\right)+\left(\frac{1}{4}-\frac{1}{4}\right)+\left(\frac{1}{6}-\frac{1}{6}\right)+...+\left(\frac{1}{2008}-\frac{1}{2008}\right)\right]+x=-\frac{1}{1005}\)\(2\cdot\left[\left(\frac{1005}{2010}-\frac{1}{2010}\right)+0+...+0\right]+x=-\frac{1}{1005}\)
\(2\cdot\frac{1004}{2010}+x=-\frac{1}{1005}\)
\(\frac{1004}{1005}+x=-\frac{1}{1005}\)
\(x=-\frac{1}{1005}-\frac{1004}{1005}=-1\)
Vậy x=-1
Chúc bạn học tốt!^_^
