1/2+1/6+1/12+1/20+1/30+1/42+1/56 怎么用四年级简便方法计算题

来源：蜘蛛抓取(WebSpider) 时间：2015-05-20 07:35 标签： 简便方法计算题
问题补充&&
列项求和1/n(n+1)=1/n-1/(n+1)如1/6=1/2*3=1/2-1/3故1/2+1/6+1/12+1/20+1/30+1/42+1/56=1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7俯户碘鞠鄢角碉携冬毛+1/7-1/8=1-1/8=7/8
小辣1987 &
1/2+1/6+1/12+1/20+1/30+1/42+1/56 =俯户碘鞠鄢角碉携冬毛1-1/2+1/2-1/3+1/3-1/4+....+1/6-1/7+1/7-1/8=1-1/8=7/8运用加法结合律。分数的分拆。
howshineyou&
1/2+1/6+1/12+1/20+1/30+1/42+1/56 =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=1-1/8=7/8
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1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=?简便算法
好心人.帮帮忙!
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=?简便算法
好心人.帮帮忙!
该式可转变为：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因为 1/2=1-1/2; 1/6=1/2-1/3; 1/12=1/3-1/4.依此类推.我还以为最先回答呢,等输完答案后才发现已有人捷足先登了,只好撤退了.1/6+1/12+1/20+1/30+1/42+1/56 简便计算_百度作业帮
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1/6+1/12+1/20+1/30+1/42+1/56 简便计算
1/6+1/12+1/20+1/30+1/42+1/56 简便计算
1/n(n+1)=1/n-1/(n+1)1/6+1/12+1/20+1/30+1/42+1/56 =1/2*3+1/3*4+……+1/7*8=1/2-1/3+1/3-1/4……+1/7-1/8=1/2-1/8=3/8
1/6+1/12+1/20+1/30+1/42+1/56 =1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7=1/2-1/7=5/14
=1/2*1/3+1/3*1/4+1/4*1/5+1/5*1/6+1/6*1/7+1/7*1/8=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8=1/2-1/8=3/8用简便方法计算1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72_百度作业帮
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用简便方法计算1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72
用简便方法计算1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72
原式=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
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1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90简便计算
1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90简便计算
1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=(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)=1/2-1/3+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=1/2-1/10=2/5
原式=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
1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=1/2*3+1/3*4+..+1/9*10=(1/2-1/3)+(1/3-1/4)+...+(1/9-1/10)=1/2-1/10=2/5
原式=1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10)=1/2-1/3+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=1/2-1/10=2/5
告诉你方法吧，1／6＝1/(2*3）＝1/2－1/3，把剩下的也化成这样就把中间的都消掉了，最后只剩一头一尾两个数了。

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