有一串数1⼀1,1⼀2,2⼀2…第2019个分数是多少

2025年04月07日 00:58
有4个网友回答
网友(1):

分母为1,2,2,3,3,3,4,4,4,4,
设等比数列的前n项和公式 n(n+1)/2=63*(63+1)/2=2016
故2016个分数的分母是63,第2017个分数的分母是64,第2018个分数的分母是64,
第2019个分数的分母是64,故第2019个分数是3/64.

网友(2):

1/1,
1/2,2/2,
1/3,2/3,3/3,
1/4,2/4,3/4,4/4,
……
按照这种方法构建分数,分母是几的分数就有几个。
(1+n)n/2=2019
(1+n)n=4038
n²+n-4038=0
解得:n≈63
从1/1到63/63一共有(1+63)x63/2=2016个分数。
2019-2016=3(个)
第2019个分数是3/64.
即,这一串分数是:1/1; 1/2,2/2; 1/3,2/3,3/3; ……1/63,2/63,3/63……63/63; 1/64,2/64,3/64.

网友(3):

解:1十2十3十……+n
=(n十1)n/2
即(n十1)n/2=2019
得:n≈63
63x64÷2=2016
2019一2016=3
故第2019个分数是3/64
答:第2019个分数是3/64

网友(4):

,2/3,3/3,2/3,1/3】……
如上分组,分母分别是1,2,3。。。n,组内数分别是:1,3,5。。。(2n-1)
分母是9时,一共有:1+3+5+。。。+(2*9-1)=81个数。
所以,第82个是1/10,则7/10是第88个。同时,第91个是10/10,则第94个也是7/10。
即7/10是第88个和第94个数。

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