Question

2004的2次方-2003的2次方+2002的2次方-2001的2次方+……2的2次方-1等于多少

Answer 1

平方差

原式=(2004+2003)(2004-2003)+(2002+2001)(2002-2001)+……+(2+1)(2-1)

=(2004+2003)×1+(2002+2001)×1+……+(2+1)×1

=2004+2003+2002+2001+……+2+1

=(2004+1)+(2003+2)+……+(1003+1002)

=2005×1002

=2009010