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计算：1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+9)(x+10)

分类: 作业答案 • 2022-01-09 18:04:27
问题描述：

计算：1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+9)(x+10)

答

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+9)(x+10)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+……+1/(x+9)-1/(x+10)
=1/x-1/(x+10)
=(x+10-x)/{x(x+10)}
= 10/{x(x+10)}

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