1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90简便计算

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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
=9/1056|评论(3)
按默认排序|按时间排序 其他回答 共4条2011-08-11 22:03O张无忌0| 十三级你好：
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/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10)
=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[提问者认可]|29|评论(12)2010-08-21 11:35IceFai| 十二级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
=9/104|评论检举|2011-08-14 17:01冰雪的泪儿| 一级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+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10)=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