神马作文网数列递推!
来源：学生作业帮 编辑：神马作文网作业帮 分类：数学作业 时间：2024/11/10 19:50:21
数列递推!
(n+1)a^2(n+1) -na^2n +a(n+1)an=0
na^2(n+1) -na^2n +a^2(n+1)+a(n+1)an=0
n[a^2(n+1) -a^2n] +a(n+1)[a(n+1)+an]=0
n[a(n+1) +an][a(n+1) -an] +a(n+1)[a(n+1)+an]=0
n[a(n+1) -an] +a(n+1)=0
na(n+1) - nan +a(n+1)=0
(n+1)a(n+1) =nan
a(n+1)/an =n/(n+1)
则有a(n)/a(n-1) =(n-1)/n
a(n-1)/a(n-2) =(n-2)/(n-1)
.
a2/a1=1/2
两边分别相乘得：
an/a1 =1/n
因为a1=1
所以an=1/n
na^2(n+1) -na^2n +a^2(n+1)+a(n+1)an=0
n[a^2(n+1) -a^2n] +a(n+1)[a(n+1)+an]=0
n[a(n+1) +an][a(n+1) -an] +a(n+1)[a(n+1)+an]=0
n[a(n+1) -an] +a(n+1)=0
na(n+1) - nan +a(n+1)=0
(n+1)a(n+1) =nan
a(n+1)/an =n/(n+1)
则有a(n)/a(n-1) =(n-1)/n
a(n-1)/a(n-2) =(n-2)/(n-1)
.
a2/a1=1/2
两边分别相乘得：
an/a1 =1/n
因为a1=1
所以an=1/n