（1+3+5+……+999）-（2+4+6+……+998）怎么简便计算

Question

（1+3+5+……+999）-（2+4+6+……+998）怎么简便计算

Answer 1

被减数 = ( 1 + 3 + 5 + 7 +……+ 999 )
= 1 + ( 2 + 1 ) + ( 4 + 1 ) + ( 6 + 1 ) +……+ ( 998 + 1 )
= 1 + ( 1X2 +1 ) + ( 2X2 +1 ) + ( 3X2 +1 ) + ……+ ( 499X2 +1 )
减数 = 2 + 4 + 6 +……+ 998
= 1X2 + 2X2 + 3X2 +……+ 449X2
结果 = 1 + 1 + 1 + 1 +……+ 1
= 1 + 499
= 500