黄冈密卷
1个回答
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用分数的拆分法来做,把题中的各个分数拆分成下面的减法算式:
1/2=1-1/2
1/6=1/2-1/3
1/12=1/3-1/4
1/20=1/4-1/5
1/30=1/5-1/6
1/42=1/6-1/7
1/56=1/7-1/8
1/72=1/8-1/9
1/90=1/9-1/10
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1-1/10
=9/10
1/2=1-1/2
1/6=1/2-1/3
1/12=1/3-1/4
1/20=1/4-1/5
1/30=1/5-1/6
1/42=1/6-1/7
1/56=1/7-1/8
1/72=1/8-1/9
1/90=1/9-1/10
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1-1/10
=9/10
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