计算 1/1x2+1/2x3+1/3x4+.+1/2009x2010

来源:学生作业帮助网 编辑:六六作业网 时间:2025/02/02 17:54:30
计算1/1x2+1/2x3+1/3x4+.+1/2009x2010计算1/1x2+1/2x3+1/3x4+.+1/2009x2010计算1/1x2+1/2x3+1/3x4+.+1/2009x20101

计算 1/1x2+1/2x3+1/3x4+.+1/2009x2010
计算 1/1x2+1/2x3+1/3x4+.+1/2009x2010

计算 1/1x2+1/2x3+1/3x4+.+1/2009x2010
1/1x2=1/1-1/2
1/2x3=1/2-1/3
1/3x4=1/3-1/4
.
1/2009x2010 =1/2009-1/2010
1/1x2+1/2x3+1/3x4+.+1/2009x2010 =(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/2009-1/2010)=1/1-1/2010=2009/2010