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\(1.2.3....2015-1.2.3....2014-1.2.3....2013.2014^2\)
\(=1.2.3...\left(2014+1\right)-1.2.3...\left(2014+1\right)\)
\(=0\)
( 2013 x 2014 +2014 x 2015 + 2015 x 2016 ) x ( 1 + 1/3 - 1 - 1/3 )
= ( 2013 x 2014 + 2014 x 2015 + 2015 x 2016 ) x 0
= 0
\(B=\frac{2014}{1}+\frac{2013}{2}+\frac{2012}{3}+....+\frac{1}{2014}\)
\(=\left(\frac{2013}{2}+1\right)+\left(\frac{2012}{3}+1\right)+....+\left(1+\frac{1}{2014}\right)+1\)
\(=\frac{2015}{2}+\frac{2015}{3}+....+\frac{2015}{2014}+\frac{2015}{2015}\)
\(=2015\left(\frac{1}{2}+\frac{1}{3}+.....+\frac{1}{2014}+\frac{1}{2015}\right)\)
\(B=\frac{2014}{1}+\frac{2013}{2}+......+\frac{1}{2014}\)
\(B=\left(\frac{2013}{2}+1\right)+\left(\frac{2012}{3}+1\right)+....+\left(\frac{1}{2014}+1\right)+1\)
\(B=\frac{2015}{2}+\frac{2015}{3}+...+\frac{2015}{2014}+\frac{2015}{2015}\)
\(B=2015\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2015}\right)\)
=3^2013:(3.3^2014)= 3^2013:3^2015=1:3^2=1/9