1/1×1/2+1/2×1/3+1/3×1/4+…+1/29×1/30

来源：学生作业帮助网编辑：六六作业网时间：2024/11/26 12:27:24

1/1×1/2+1/2×1/3+1/3×1/4+…+1/29×1/301/1×1/2+1/2×1/3+1/3×1/4+…+1/29×1/301/1×1/2+1/2×1/3+1/3×1/4+…+1/29

1/1×1/2+1/2×1/3+1/3×1/4+…+1/29×1/30
1/1×1/2+1/2×1/3+1/3×1/4+…+1/29×1/30

1/1×1/2+1/2×1/3+1/3×1/4+…+1/29×1/30
=1+（1-1/2）+（1/2-1/3）+（1/3-1/4）+……+（1/29-1/30）
=1+1-1/30
=59/30
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