灵鹊做题网｜1/2-1｜+｜1/3-1/2｜+｜1/4-1/3｜+｜1/5-1/4｜+.+｜1/2012-1/2011｜这题如何解
来源：学生作业帮 编辑：灵鹊做题网作业帮 分类：数学作业 时间：2024/05/15 23:14:10
｜1/2-1｜+｜1/3-1/2｜+｜1/4-1/3｜+｜1/5-1/4｜+.+｜1/2012-1/2011｜这题如何解啊.注：1/2表示二分之一.
｜1/2-1｜+｜1/3-1/2｜+｜1/4-1/3｜+｜1/5-1/4｜+.+｜1/2012-1/2011｜
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5.+1/2011-1/2012
=1+(-1/2+1/2)+(-1/3+1/3)+(-1/4+1/4)+(-1/5+1/5)+.+(-1/2011)1/2011)-1/2012
=1+0+0+0+0+.+0-1/2012
=1-1/2012
=2011/2012
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5.+1/2011-1/2012
=1+(-1/2+1/2)+(-1/3+1/3)+(-1/4+1/4)+(-1/5+1/5)+.+(-1/2011)1/2011)-1/2012
=1+0+0+0+0+.+0-1/2012
=1-1/2012
=2011/2012