Question

tính nhanh: 1/ 2002 x 2003 + 1/ 2003 x 2005 + ... + 1/ 2011 x 2013

 

 

Answer 1

\(\frac{1}{2001\cdot2003}+\frac{1}{2003\cdot2004}+...+\frac{1}{2011\cdot2013}\)

\(=\frac{1}{2}\left(\frac{2}{2001\cdot2003}+\frac{2}{2003\cdot2005}+...+\frac{2}{2011\cdot2013}\right)\)

\(=\frac{1}{2}\left(\frac{1}{2001}-\frac{1}{2003}+\frac{1}{2003}-\frac{1}{2005}+...+\frac{1}{2011}-\frac{1}{2013}\right)\)

\(=\frac{1}{2}\left(\frac{1}{2001}-\frac{1}{2013}\right)\)

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