早教吧作业答案频道 -->其他-->
在数列an中,已知a1=1,a(n+2)=1/(an+1),a100=a96,则a9+a10=?
题目详情
在数列an中,已知a1=1,a(n+2)=1/(an+1),a100=a96,则a9+a10=?
▼优质解答
答案和解析
a9 = 1/(a7 +1)
= 1/[ 1/(a5+1) +1 ]
= (a5+1)/(a5+2)
= [ 1/(a3+1) +1 ]/[ 1/(a3+1) + 2]
= (a3+2)/(a3+3)
= (a1+3)/(a1+4)
= 4/5
a100= 1/(a98+1)
= 1/[1/(a96+1) + 1]
= (a100+1)/(a100+2)
(a100)^2+a100-1=0
a100=(-1+ √5)/2
a12 =a100= (-1+ √5)/2
a12 = 1/(a10 +1)
(-1+ √5)/2 =1/(a10 +1)
(-1+ √5)(a10 +1) = 2
a10 = (3-√5)/(-1+√5)
= (3-√5).(1+√5)/ 4
= (-1+√5)/2
a9+a10 = 4/5 + (-1+√5)/2
= 1/[ 1/(a5+1) +1 ]
= (a5+1)/(a5+2)
= [ 1/(a3+1) +1 ]/[ 1/(a3+1) + 2]
= (a3+2)/(a3+3)
= (a1+3)/(a1+4)
= 4/5
a100= 1/(a98+1)
= 1/[1/(a96+1) + 1]
= (a100+1)/(a100+2)
(a100)^2+a100-1=0
a100=(-1+ √5)/2
a12 =a100= (-1+ √5)/2
a12 = 1/(a10 +1)
(-1+ √5)/2 =1/(a10 +1)
(-1+ √5)(a10 +1) = 2
a10 = (3-√5)/(-1+√5)
= (3-√5).(1+√5)/ 4
= (-1+√5)/2
a9+a10 = 4/5 + (-1+√5)/2
看了 在数列an中,已知a1=1,...的网友还看了以下：
已知函数f(x)=x/(2*x+1),数列{an}满足a[1]=1/2,a[n+1]=f(a[n] 2020-05-13 …
数列a[n+1]=k+(2k+1)a[n]+(k(k+1)a[n](a[n+1]))^1/2 已知 2020-05-16 …
数列a[n+1]=k+(2k+1)a[n]+(k(k+1)a[n]a[n+1])^1/2 已知a1 2020-05-16 …
1、等比数列中,知道a3=1,S3=13,怎么得出q=1/3?2、已知nS(n+1)>(n+1)S 2020-06-04 …
数列怎么这么难!1.已知a(1)=3且a(n)=S(n-1)+2^n,求an及Sn.2.已知S(n 2020-06-04 …
已知a1=1,an=n(a(n+1)-an),则数列{an}的通项公式an为————（1,n,n+ 2020-06-06 …
1.已知数列{a(n)}满足a(n)a(n+1)a(n+2)a(n+3)=24,且a1=1a2=2 2020-07-09 …
1、已知数列{An}满足：A1=1,A2=1/2,且[3+(-1)^n]A-2An+2[(-1)^ 2020-08-01 …
已知数列｛an｝满足a1=1,(a(n-1)+1)/an=(a(n-1)+1)/(1-an),(n∈ 2020-11-19 …
有关等差数列,1、已知数列{an}的首项a(1)=1,且an＝2a(n-1)＋1n＞＝2,则a(5) 2020-12-07 …