[tex]\displaystyle\bf\\1+3+5+...+2021=?\\\\\textbf{Calculam numarul de termeni (n).}\\\\n=\frac{2021-1}{2}+1=\frac{2020}{2}+1=1010+1\\\\ \boxed{\bf~n=1011~termeni}\\\\Aplicam~formula~lui~Gauss:\\\\S=1+3+5+...+2021=\frac{n(2021+1)}{2}\\\\S=\frac{1011(2022)}{2}=1011\times1011 \\\\\boxed{\bf~S=1011^2}\\\\\boxed{\bf~S=1022121}[/tex]
