\(\dfrac{1}{2001\times2003}+\dfrac{1}{2003\times2005}+...+\dfrac{1}{2011\times2013}\)
\(=\dfrac{1}{2}\cdot\left(\dfrac{2}{2001\times2003}+\dfrac{2}{2003\times2005}+...+\dfrac{2}{2011\times2013}\right)\)
\(=\dfrac{1}{2}\cdot\left(\dfrac{1}{2001}-\dfrac{1}{2003}+\dfrac{1}{2003}-...+\dfrac{1}{2011}-\dfrac{1}{2013}\right)\)
\(=\dfrac{1}{2}\cdot\left(\dfrac{1}{2001}-\dfrac{1}{2013}\right)\)
\(=\dfrac{1}{2}\cdot\dfrac{4}{1342671}\)
\(=\dfrac{2}{1342671}\)
\(\dfrac{1}{2001\times2003}+\dfrac{1}{2003\times2005}+\dfrac{1}{2005\times2007}+...+\dfrac{1}{2011\times2013}\) (sửa đề)
\(=\dfrac{1}{2}\times\left(\dfrac{2}{2001\times2003}+\dfrac{2}{2003\times2005}+\dfrac{2}{2005\times2007}+...+\dfrac{2}{2011\times2013}\right)\)
\(=\dfrac{1}{2}\times\left(\dfrac{1}{2001}-\dfrac{1}{2003}+\dfrac{1}{2003}-\dfrac{1}{2005}+\dfrac{1}{2005}-\dfrac{1}{2007}+...+\dfrac{1}{2011}-\dfrac{1}{2013}\right)\)
\(=\dfrac{1}{2}\times\left(\dfrac{1}{2001}-\dfrac{1}{2013}\right)\)
\(=\dfrac{1}{2}\times\dfrac{4}{1342671}\)
\(=\dfrac{2}{1342671}\)
