1 = 1+2 x 0
3 = 1+2 x 1
5 = 1+2 x 2
.....................
2011= 1+ 2 x 1005
_______________
1+3+5+...+2011 = 1+1+..+1+2x(0+1+2+3+..+1005)
de 1006 ori
1+3+5+...+2011 = 1006 x 1 + 2 x 1005 x 1006 :2
= 1006 + 1005 x 1006
=1006x(1+1005)
= 1006 x 1006
= 1006²
=1012036