[tex]\displaystyle\bf\\a=\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+\frac{4}{5}+\frac{5}{6}+\frac{6}{7}\\\\b=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}\\\\......................................................... le~adunam\\\\a+b=\frac{1}{2}+\frac{1}{2}+\frac{2}{3}+\frac{1}{3}+\frac{3}{4}+\frac{1}{4}+\frac{4}{5}+\frac{1}{5}+\frac{5}{6}+\frac{1}{6}+\frac{6}{7}+\frac{1}{7}=\\\\a+b=\frac{1+1}{2}+\frac{2+1}{3}+\frac{3+1}{4}+\frac{4+1}{5}+\frac{5+1}{6}+\frac{6+1}{7}[/tex]
[tex]\displaystyle\bf\\a+b=\frac{2}{2}+\frac{3}{3}+\frac{4}{4}+\frac{5}{5}+\frac{6}{6}+\frac{7}{7}\\\\a+b=1+1+1+1+1+1\\\\a+b=6\times1\\\\\boxed{\bf~a+b=6}\\\\a+2014+b=a+b+2014=6+2014=\boxed{\bf2020}[/tex]
