1/10+2/20+3/30+4/40+5/50+6/60+7/70+8/80+9/90
=1/10+1/10+1/10+1/10+1/10+1/10+1/10+1/10+1/10
=1/10*9=9/10
=1/10+1/10+1/10+1/10+1/10+1/10+1/10+1/10+1/10
=1/10x9
=9/10
\(\frac{1}{10}+\frac{2}{20}+\frac{3}{30}+\frac{4}{40}+\frac{5}{50}+\frac{6}{60}+\frac{7}{70}+\frac{8}{80}+\frac{9}{90}\)
\(=\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}\)
\(=9\times\frac{1}{10}\)
\(=\frac{9}{10}\)