[tex]\displaystyle \boxed{ \frac{n(n+1)}{2} } \\ \\\text{Suma lui Gaus: n e ultimul numar din sir, se aplica la sirul 1+2+3+...} \\ \\ \\ 5+10+15+.....+2010= \\ \text{Se da 5 factor comun, adica pui 5 in fata si ce ramane e impartit la 5} \\ \\ 5(1+2+3+...+402)= \\\\ \frac{n(n+1)}{2} = \frac{402(402+1)}{2} = \frac{402 \cdot403}{2} = 201 \cdot 403 = 81.003 \\ \\ 5\cdot81.003=\boxed{\boxed{405.015}}[/tex]
