计算:1/m(m+1)+1/(m+1)(m+2)+1/(m+2)(m+3)+1/(m+3)(m+4)+1/(m+4)(m+5)+.+1/(m+9)(m+10)
来源:学生作业帮助网 编辑:作业帮 时间:2024/09/02 07:32:04
计算:1/m(m+1)+1/(m+1)(m+2)+1/(m+2)(m+3)+1/(m+3)(m+4)+1/(m+4)(m+5)+.+1/(m+9)(m+10)
计算:1/m(m+1)+1/(m+1)(m+2)+1/(m+2)(m+3)+1/(m+3)(m+4)+1/(m+4)(m+5)+.+1/(m+9)(m+10)
计算:1/m(m+1)+1/(m+1)(m+2)+1/(m+2)(m+3)+1/(m+3)(m+4)+1/(m+4)(m+5)+.+1/(m+9)(m+10)
1/m(m+1)=1/m-1/(m+1)
裂项法
所以原式=1/m-1/(m+1)+1/(m+1)-1/(m+2)+……+1/(m+9)-1/(m+10)
=1/m-1/(m+10)
=10/m(m+10)
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