\(=0,1+0,1+0,1+0,1+0,1+0,1+0,1+0,1+0,1=0,1\times9=0,9\)
\(\dfrac{1}{10}+\dfrac{2}{20}+\dfrac{3}{30}+\dfrac{4}{40}+\dfrac{5}{50}+\dfrac{6}{60}+\dfrac{7}{70}+\dfrac{8}{80}+\dfrac{9}{90}\)
\(=\dfrac{1}{10}+\dfrac{1}{10}+\dfrac{1}{10}+\dfrac{1}{10}+\dfrac{1}{10}+\dfrac{1}{10}+\dfrac{1}{10}+\dfrac{1}{10}+\dfrac{1}{10}\)
\(=\dfrac{1+1+1+1+1+1+1+1}{10}\)
\(=\dfrac{9}{10}\)
\(\left(\dfrac{1}{10}+\dfrac{9}{90}\right)+\left(\dfrac{2}{20}+\dfrac{8}{80}\right)+\left(\dfrac{3}{30}+\dfrac{7}{70}\right)+\left(\dfrac{4}{40}+\dfrac{6}{60}\right)+\dfrac{5}{50}\)
\(=\dfrac{1}{5}+\dfrac{1}{5}+\dfrac{1}{5}+\dfrac{1}{5}+\dfrac{5}{50}\)
\(=1+\dfrac{5}{50}\)
= \(\dfrac{55}{50}=\dfrac{11}{10}\)