[tex]\displaystyle\bf\\f)\\\\Nu~este~necesar~sa~calculam~sumele~cu~Gauss.\\\\(6+12+18+...+600)^2:(3+6+9+...+300):(1+2+3+...+100)=\\\\=\frac{(6+12+18+...+600)^2}{(3+6+9+...+300)}:(1+2+3+...+100)=\\\\\\=\frac{[2(3+6+9+...+300)]^2}{(3+6+9+...+300)}:(1+2+3+...+100)=\\\\\\=\frac{2^2(3+6+9+...+300)^2}{(3+6+9+...+300)}:(1+2+3+...+100)=\\\\=4(3+6+9+...+300)^{2-1}:(1+2+3+...+100)=\\\\=\frac{4(3+6+9+...+300)}{(1+2+3+...+100)}=\\\\\\=\frac{4\times3\times(1+2+3+...+100)}{(1+2+3+...+100)}=4\times3=\boxed{\bf12}[/tex]
