已知集合{1,2},{3,4,5,6,},{7,8,9,10,11,12,13,14},…,其中第n个集合有2^n个连续正整数组成,并且每一个

2024年12月04日 04:58
有4个网友回答
网友(1):

第一题不用了吧亲2^(n+1)-2
(2)
b1=2^2/(a1*a2)=4/12=1/3;b2=2^3/(a2*a3)=8/84=2=21……
bn=2^(n+1)/(2^(n+1)-2)*(2^(n+2)-2) = (2^n/(2^(n+1)-2))-2^n/(2^(n+2)-2))*1/(2^n)
比如b1=(4/2-6/2)*1/4 ,b2=(8/6-8/14)*1/8
那么Sn=(1/2-1/6)+(1/6-1/14)+(1/14-1/30)……+(1/(2^(n+1)-2)-1/(2^(n+2)-2))
=1/2-1/(2^(n+2)-2)
Sn最小值为1/2-1/6=1/3
无最大值无限接近1/2
∴根据题意得a应该等于1/3

纯手打哦亲~其实本来也想来查的自己突然想出来了 跪求采纳

网友(2):

(1)由于第n个集合中有2的n次方(2^n)个元素,而且集合集合之间的元素是连续的,所以第n个集合中最大的数an=2^1+2^2+......+2^n=2^(n+1) - 2
(2)...

网友(3):

(2)中先把bn的表达式化简,然后观察b1+b2+……bn,化简然后求范围。

网友(4):

an=2的(n-2)次方

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