计算：1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2006)(a+2007)

来源：学生作业帮编辑：拍题作业网作业帮分类：数学作业时间：2024/04/28 00:03:48

计算：1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2006)(a+2007)
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裂项：1/a(a+1)=1/a-1/(a+1)
1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2006)(a+2007)
=1/a-1/(a+1)+1/(a+1)-1/(a+2)+...+1/(a+2006)-1/(a+2007)
=1/a-1/(a+2007)

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