1/30+1/42+1/56+1/72+1/90的最简便算法

分类: 作业答案 • 2022-02-19 13:55:47

问题描述：

答

1/30+1/42+1/56+1/72+1/90
=1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1/5-1/10
=1/10

答

上式等于：(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)+(1/9-1/10)=1/5-1/10=1/10

答

1/30=1/（5×6）=1/5-1/6
1/42=1/（6×7）=1/6-1/7
……
1/30+1/42+1/56+1/72+1/90
=1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1/5-1/10
=1/10