计算1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2007)(a+2008)+1/(a+2011)(a+

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/13 11:11:15

计算1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2007)(a+2008)+1/(a+2011)(a+2012)

1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2007)(a+2008)+1/(a+2011)(a+2012)
=1/a-1/(a+1)+1/(a+1)-1/(a+2)+...+1/(a+2007)-1/(a+2008)+1/(a+2011)-1/(a+2012)
=1/a-1/(a+2012)
=2012/[a(a+2012)]

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