l1/2-1l+l1/3-1/2l+l1/4-1/3l+...+l1/2008-1/2007l+l1/2009l-1/2008l

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/10 19:27:34
l1/2-1l+l1/3-1/2l+l1/4-1/3l+...+l1/2008-1/2007l+l1/2009l-1/2008l

l1/2-1l+l1/3-1/2l+l1/4-1/3l+...+l1/2008-1/2007l+l1/2009l-1/2008l
l1/2-1l+l1/3-1/2l+l1/4-1/3l+...+l1/2008-1/2007l+l1/2009l-1/2008l

l1/2-1l+l1/3-1/2l+l1/4-1/3l+...+l1/2008-1/2007l+l1/2009l-1/2008l
由于被减数都小于减数
所以
原式=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/2007-1/2008+1/2008-1/2009
可以发现,中间的全部可以抵消.
=1-1/2009
=2008/2009

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