1/2+5/6+11/12+19/20+.+89/90+109/110 答案是多少,还有要写明这里有几项?

问题描述:

1/2+5/6+11/12+19/20+.+89/90+109/110 答案是多少,还有要写明这里有几项?
1个回答 分类:数学 2014-10-24

问题解答:

我来补答
1/2+5/6+11/12+19/20+.+89/90+109/110
=1-1/2+1-1/6+1/1/12+1-1/20+……+1-1/90+1-1/110
=10-(1/2+1/6+1/12+1/20+……+1/90+1/110)
=10-(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/9-1/10+1/10-1/11)
=10-(1-1/11)
=9+1/11
=9又1/11
再问: 是哪十项啊?
再答: 1/2+5/6+11/12+19/20+29/30+41/42+55/56+71/72+89/90+109/110 =1-1/2+1-1/6+1/1/12+1-1/20+……+1-1/90+1-1/110 =10-(1/2+1/6+1/12+1/20+……+1/90+1/110) =10-(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/9-1/10+1/10-1/11) =10-(1-1/11) =9+1/11 =9又1/11
 
 
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