[tex]3+6+9+...+333 = \\ \\ 3\times(1+2+3+...+111) = \\ \\ = 3\times\dfrac{111\times(111+1)}{2} = \\ \\ =3\times \dfrac{111\times 112}{2} = \\ \\ = 3\times 111\times 56 = \\ \\ =18648[/tex]
[tex]2+5+8+...+149 = \\ $(creste din 3 in 3, o sa avem ca factor pe 3)\\ \\ $ =(3\times1-1)+ (3\times 2-1)+(3\times 3-1)+...+(3\times 50-1) =\\ \\ = 3\times(1+2+3+...+50)-1\times 50 = \\ \\ = 3\times \dfrac{50\times 51}{2}-50 = \\ \\ = 3\times 25\times 51-25\times 2 \\ \\ = 25\times (3\times 51-2) = \\ \\ =25\times (153-2) = \\ \\ = 25\times 151 = \\ \\ = 3775[/tex]
