作业帮计算1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2007)(a+2008)
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/06 03:10:58
计算1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2007)(a+2008)
计算1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2007)(a+2008)
计算1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2007)(a+2008)
列项,
1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2007)(a+2008)
=1/a-1/(a+1)+1/(a+1)-1/(a+2)..-1/(a+2008)
=1/a-1/(a+2008)
=2008/(a*(a+2008))
=1/a-1/(a+1)+1/(a+1)-1/(a+2)+……+1/(a+2007)-1/(a+2008)=1/a-1/(a+2008)=2008/[a(a+2008)]
1/a（a+1）=1/a-1/(a+1)
所以1/a（a+1）+1/(a+1)(a+2)+...+1/(a+2007)(a+2008)=1/a-1/(a+1)+1/(a+1)-1/(a+2)+...+1/(a+2007)-1/(a+2008)中间项消掉了
=1/a-1/(a+2008)=2008/a(a+2008)
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