计算1/20002002+1/20022004+1/20042006+1/20062008+1/2008*2010

分类: 作业答案 • 2021-12-19 15:53:30

问题描述：

计算1/2000*2002+1/2002*2004+1/2004*2006+1/2006*2008+1/2008*2010

答

1/2×（1/2000-1/2002+1/2002-1/2004+……+1/2008-1/2010）=1/2×（1/2000-1/2010）=401/804000

答

原式=(（1/2000-1/2002）+(1/2002-1/2004)+(1/2004-1/2006)+(1/2006-1/2008)+(1/2008-1/2010))/2
=(1/2000-1/2010)/2
=5/2000*2010
=5/4020000
=1/804000

计算1/2000*2002+1/2002*2004+1/2004*2006+1/2006*2008+1/2008*2010