[tex]\displaystyle \\
1+2+3+4+.......+75+76-1-2-3-.....-29-30= \\
= 31+32+32+ ....... +75+76 \\ \\
\texttt{Aplicam formula lui Gaus: } \\ \\
S= \frac{\text{Numarul de termeni } \times ~\text{(Ultimul termen + Primul termen)} }{2} \\ \\
\texttt{Numarul de termeni } = 76-31+1 = 45+1=46~termeni \\ \\
31+32+32+ ....... +75+76 = \frac{46(76+31)}{2} = \\ \\
=23(76+31)= 23 \times 107 = \boxed{ 2461 }
[/tex]
