[tex]\displaystyle\\\frac{1}{7}+\frac{2}{7}+\frac{3}{7}+\cdots+\frac{20}{7}=\\\\\frac{1}{7}\Big(1+2+3+\cdots+20\Big)=~~~~~\text{Folosim formula lui Gauss}\\\\=\frac{1}{7}\times\frac{20(20+1)}{2}=\frac{1}{7}\times\frac{20\times21}{2}=\frac{1}{7}\times10\times21=\frac{210}{7}=\boxed{30}[/tex]
