1+(-2)+(+3)+(-4)+(+5)+...+(-2008)+(+2009)

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1+(-2)+(+3)+(-4)+(+5)+...+(-2008)+(+2009)

1+(-2)+(+3)+(-4)+^+(-2008)+(2009)
=1-2+3-4+^-2008+2009
=(1-2)+(3-4)+^+(2007-2008)+2009
=-1-1-1-1-^-1+2009
=-1004*1+2009
=1005