Metoda I:
[tex]S = 1\,\,\,+2\,\,\,+3\,\,\,+...+84 \\ S = 84+83+82+...+1\\\noindent\rule{4.96cm}{0.7pt}\\2S = 85+85+85+\underbrace{...}\limits_{de\, 84\, ori}+85 \\ 2S = 84\cdot 85\\ \\ S = \dfrac{84\cdot 85}{2} \\ \\ S = 42\cdot 85 \\ \\ \Rightarrow \boxed{S = 3570}[/tex]
Metoda II:
[tex]\boxed{1+2+3+...+n = \dfrac{n(n+1)}{2}}\quad -\text{Suma lui Gauss}\\ \\ \\ 1+2+3+...+84 = \dfrac{84\cdot (84+1)}{2} =\dfrac{84\cdot 85}{2} = 42\cdot 85 = 3570[/tex]
