作业帮1/2*4+1/6*8+······+1/2006*2008+1/4*6+1/8*10+······+1/2004*20
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/12 16:25:57
1/2*4+1/6*8+······+1/2006*2008+1/4*6+1/8*10+······+1/2004*2006=?
*是乘号 /是分数线
*是乘号 /是分数线
1/2*4+1/6*8+······+1/2006*2008+1/4*6+1/8*10+······+1/2004*2006
=1/2*4+1/4*6+1/6*8+18*10+······+1/2004*2006+1/2006*2008
=1/2*(1/2-1/4)+1/2*(1/4-1/6)+1/2*(1/6-1/8)+1/2*(1/8-1/10)+.+1/2*(1/2004-1/2006)+1/2*(1/2006-1/2008)
=1/2*(1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10+.+1/2004-1/2006+1/2006-1/2008)
=1/2*(1/2-1/2008)
=1/2*(1004/2008-1/2008)
=1/2*1003/2008
=1003/4016
=1/2*4+1/4*6+1/6*8+18*10+······+1/2004*2006+1/2006*2008
=1/2*(1/2-1/4)+1/2*(1/4-1/6)+1/2*(1/6-1/8)+1/2*(1/8-1/10)+.+1/2*(1/2004-1/2006)+1/2*(1/2006-1/2008)
=1/2*(1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10+.+1/2004-1/2006+1/2006-1/2008)
=1/2*(1/2-1/2008)
=1/2*(1004/2008-1/2008)
=1/2*1003/2008
=1003/4016
1/2*4+1/6*8+······+1/2006*2008+1/4*6+1/8*10+······+1/2004*20
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