1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=? 用简便算法算

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1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=? 用简便算法算
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1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=? 用简便算法算
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=? 用简便算法算

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=? 用简便算法算
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
=1/7-1/8
=1/8-1/9
=1/9-1/10
所以原式=1/2+1/2-1/10
=9/10

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=1/1*2+1/2*3+1/3*4+....+1/9*10
=1-1/2+1/2-1/3+1/3-1/4+...+1/8-1/9+1/9-1/10
=1-1/10
=9/10