f(x)=1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+.1/(x+9)(x+10) 求

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/10 14:11:18

f(x)=1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+.1/(x+9)(x+10) 求f(8)

f(x)=1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+.1/(x+9)(x+10)
=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)+.+1/(x+9)-1/(x+10)
=1/(x+1)-1/(x+10)
属于裂项求和
∴ f(8)=1/9-1/18=1/18

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