Question

2009^2-2007^2+2005^2+2003^2+.+5^2-3^2+1^2

Answer 1

=2*(2009+2007）+2(2005+2003)+...+2(9+7)+2(5+3)+1

=2*(4016+4008+4000+3992+...+16+8)+1

a1=8,d=8,an=4016

8+(n-1)*8=4016

n=4016/8=502

S502=1+(8+4016)*502/2=1+4024*251

=1010025