Question

    So sánh các phân số sau:

Answer 1

\(\dfrac{2011\cdot2012}{2011\cdot2012+1}=\dfrac{2011\cdot2012+1-1}{2011\cdot2012+1}=1-\dfrac{1}{2011\cdot2012+1}\)

\(\dfrac{2012\cdot2013}{2012\cdot2013+1}=\dfrac{2012\cdot2013+1-1}{2012\cdot2013+1}=1-\dfrac{1}{2012\cdot2013+1}\)

Ta có: \(2011\cdot2012< 2012\cdot2013\)

=>\(2011\cdot2012+1< 2012\cdot2013+1\)

=>\(\dfrac{1}{2011\cdot2012+1}>\dfrac{1}{2012\cdot2013+1}\)

=>\(-\dfrac{1}{2011\cdot2012+1}< \dfrac{-1}{2012\cdot2013+1}\)

=>\(\dfrac{-1}{2011\cdot2012}+1< \dfrac{-1}{2012\cdot2013+1}+1\)

=>\(\dfrac{2011\cdot2012}{2011\cdot2012+1}< \dfrac{2012\cdot2013}{2012\cdot2013+1}\)