[tex]\displaystyle 1+3+5+7+...+2011 \\ 2011=1+(n-1) \cdot 2 \\ 2011=1+2n-2 \\ 2n=2011-1+2 \\ 2n=2012 \\ n=2012:2 \\ n=1006 \\ S_{1006}= \frac{2+1005 \cdot 2}{2} \cdot 1006 \\ \\ S_{1006}= \frac{2+2010}{2} \cdot 1006 \\ \\ S_{1006}= \frac{2012}{2} \cdot1006 \\ \\ S_{1006}=1006 \cdot 1006 \\ S_{1006}=1012036[/tex]
