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循環性遞迴數列 {an}

an=an1+1an2,n≧3


(一):1,1,2,3,2,1,1,2,3,2,1,1,2,3,2,...
(二)2,3,2,1,12,3,2,1,12,3,2,1,1,...
(三):3,2,1,1,2,3,2,1,1,2,3,2,1,1,2,...

a3=a2+1a1
a4=a3+1a2=a2+1a1+1a2=a1+a2+1a1a2
a5=a4+1a3=a1+a2+1a1a2+1a2+1a1=(a1+1)(a2+1)a1a2a2+1a1=a1+1a2

a6=a5+1a4=a1+1a2+1a1+a2+1a1a2=a1

a7=a6+1a5=a1+1a1+1a2=a2

得知數列 {an}是前5項循環的數列

數列 {an}的第一項a1 = 第二項a2=   (a1和a2都是正整數)

列出前 n 項,n= ( n ≧ 3 )       

                                          

( n ≧ 3
,如果
an-2 不能整除an-1+1,則an取近似值到小數1位  )

   

 

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