[tex]\displaystyle 1+3+5+...+2013 \\ \\ 2013=1+(n-1) \times 2 \\ \\ 2013=1+2n-2 \\ \\ 2n=2013-1+2 \\ \\ 2n=2014 \\ \\ n= \frac{2014}{2} \\ \\ n=1007[/tex]
[tex]\displaystyle S_{1007}= \frac{2+1006 \times 2}{2} \times 1007 \\ \\ S_{1007}= \frac{2+2012}{2} \times 1007 \\ \\ S_{1007}= \frac{2014}{2} \times 1007 \\ \\ S_{1007}=1007 \times 1007 \\ \\ S_{1007}=1014049[/tex]
