Question

Calculati: 1+2+3+4+......+75+76-1-2-3-.....-29-30=?

Answer 1

   
[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]