Question

已知有序数组（a,b,c,d），现按下列方式重新写成数组（a1,b1,c1,d1）使a1=a+b,b1=a+c

已知一个有序数组（A,B,C,D),现按下列方式重新写成数组(A1,B1,C1,D1),使
A1=A+B, B1=A+C, C1=C+D, D1=D+A, 按照这个规律继续写出(A2,B2,C2,D2)……，（An,Bn,Cn,Dn),若 1000<（An+Bn+Cn+Dn）÷（A+B+C+D）<2000, 则 n=_______.
麻烦详细一点，不要只是敷衍的几句话，最好有过程

Answer 1

由题目所给的数据关系，我们可以采用特值法：
具体如下
你把A B C D全部都令为1
则A0数组的和B0=4
A1。。。B1=8
A2。。。B2=16
。。。。。。。每次相当于扩大一倍。
Bn =4*2^n (n=0,1,2,3....)
所以1000<Bn/4<2000
___有 4000<Bn<8000
所以 1000<2^n<2000
因为2^10=1024
2^11=2048

所以n=10

希望你会采纳，谢谢你！

Answer 2

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Answer 3

假设A+B+C+D=M
则A1+B1+C1+D1=A+B+A+C+C+D+D+A=2M
同理，An+Bn+Cn+Dn=2^n*M
由1000<（An+Bn+Cn+Dn）÷（A+B+C+D）<2000
得1000<2^n<2000
n=10

祝你学习愉快！

追问

为什么A+B+A+C+C+D+D+A=2M?A+B+A+C+C+D+D+A=3A+B+2C+4D≠2A+2B+2C+2D

追答

是你写错了吧，B1=B+C吧

追问

没写错，书上就是这样

追答

如果真是这样，那这个题就不能解了，我敢肯定这是书上打印错误！