2012²-2011²+2010²-2009²+…+4²-3²+2²-1
=(2012²-2011²)+(2010²-2009²)+…+(4²-3²)+(2²-1)
=(2012+2011)(2012-2011)+(2010+2009)(2010-2009)+...+(4+3)(4-3)+(2+1)(2-1)
=2012+2011+2010+2009+...+4+3+2+1
=(2012+1)X2012/2
=2025078