\(\frac{2011}{2010}\times\frac{2012}{2011}\times\frac{2013}{2012}\times\frac{2014}{2013}\times\frac{1005}{1007}\)
\(=\frac{2014}{2010}\times\frac{1005}{1007}\)
\(=\frac{2\times1007\times1005}{2\times1005\times1007}\)
\(=1\)
\(\frac{2011}{2010}\cdot\frac{2012}{2011}\cdot\frac{2013}{2012}\cdot\frac{2014}{2013}\cdot\frac{2010}{2014}\)
\(=\frac{2010\cdot2011\cdot2012\cdot2013\cdot2014}{2010\cdot2011\cdot2012\cdot2013\cdot2014}\)
= 1
\(\frac{2011}{2010}.\frac{2012}{2011}.\frac{2013}{2012}.\frac{2014}{2013}.\frac{1005}{1007}=\frac{2014}{2010}.\frac{1005}{1007}\)
\(\frac{2014}{2010}.\frac{1005}{1007}=\frac{1007}{1005}.\frac{1005}{1007}=1\)
\(\frac{2011}{2010}×\frac{2012}{2011}×\frac{2013}{2012}×\frac{2014}{2013}×\frac{1005}{1007}\)
\(=\frac{2012}{2010}×\frac{2014}{2012}×\frac{1005}{1007}\)
\(=\frac{2014}{2010}×\frac{1005}{1007}\)
\(=\frac{1007}{1005}×\frac{1005}{1007}\)
\(=\frac{1007×1005}{1005×1007}\)
\(=1\)
Làm:
\(\frac{2011}{2010}\cdot\frac{2012}{2011}\cdot\frac{2013}{2012}\cdot\frac{2014}{2013}\cdot\frac{1005}{1007}\)
\(=\frac{2012}{2010}\cdot\frac{2014}{2012}\cdot\frac{2005}{1007}\)
\(=\frac{2014\cdot2005}{2010\cdot1007}\) (sau đó rút gọn phân số và ra kết quả)
\(=1\)
\(\frac{2011}{2010}\times\frac{2012}{2011}\times\frac{2013}{2012}\times\frac{2014}{2013}\times\frac{1005}{1007}\)
\(=\left[\left(\frac{2011}{2010}\times\frac{2012}{2011}\right)\times\left(\frac{2013}{2012}\times\frac{2014}{2013}\right)\right]\times\frac{1005}{1007}\)
\(=\left(\frac{2012}{2010}\times\frac{2014}{2012}\right)\times\frac{1005}{1007}\)
\(=\frac{2014}{2010}\times\frac{1005}{1007}\)
\(=\frac{1007}{1005}\times\frac{1005}{1007}\)
\(=1\)
