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

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/04 02:35:59
计算1/2000*2002+1/2002*2004+1/2004*2006+1/2006*2008+1/2008*2010

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

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

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