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1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3 )+……+1/(a+2009)(a+2010)

分类: 作业答案 • 2022-01-09 18:02:09
问题描述：

1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3 )+……+1/(a+2009)(a+2010)

答

1/a(a+1)+1/(a+1)(a+2)+1/(a+2)(a+3 )+……+1/(a+2009)(a+2010)=1/a-1/(a+1)+1/(a+1)-1/(a+2)+1/(a+2)-1/(a+3 )+……+1/(a+2009)-1/(a+2010)=1/a-1/(a+2010)=2010/[a(a+2010)]

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