3/4+1/20+1/30+1/42+1/56+1/72 求如何简便点的计算

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3/4+1/20+1/30+1/42+1/56+1/72 求如何简便点的计算
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3/4+1/20+1/30+1/42+1/56+1/72 求如何简便点的计算
3/4+1/20+1/30+1/42+1/56+1/72 求如何简便点的计算

3/4+1/20+1/30+1/42+1/56+1/72 求如何简便点的计算
3/4+1/20+1/30+1/42+1/56+1/72
=(1-1/4)+(1/4-1/5)+(1/5-1/6)+(6/1-1/7)+(1/7-1/8)+(1/8-1/9)
=1-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9
=1-1/9
=8/9

3/4+1/20+1/30+1/42+1/56+1/72 求如何简便点的计算
解,得:
==1-(1/4)+[(1/4)-(1/5)]+[(1/5)-(1/6)]+[(1/6)-(1/7)]+[(1/7)-(1/8)]+[(1/8)-(1/9)]
==1-(1/9)
==8/9