数列an满足a1=1/3,Sn=n(2n-1)an,求an

来源：学生作业帮编辑：大师作文网作业帮分类：数学作业时间：2024/11/16 23:28:05

Sn=n(2n-1)an,S(n+1)=(n+1)[2(n+1)-1]a(n+1)
=(n+1)[2n+1]a(n+1)
S(n+1)-Sn=a(n+1)
即(n+1)[2n+1]a(n+1)-n(2n-1)an=a(n+1)
n(2n-1)an=（2n^2+3n）a(n+1)
(2n-1)an=（2n+3）a(n+1)
a(n+1)=(2n-1)/（2n+3）an a2=1/5*1/3=1/15
=(2n-1)/（2n+3）*(2n-3)/（2n+1）a(n-1)
=(2n-1)/（2n+3）*(2n-3)/（2n+1）*(2n-5)/（2n-1）a(n-2)
.
=(2n-1)/（2n+3）*(2n-3)/（2n+1）*(2n-5)/（2n-1）*...*1/5a1
=(2n-1)/（2n+3）*(2n-3)/（2n+1）*(2n-5)/（2n-1）*...*1/5*1/3
=1/[（2n+3）（2n+1）]
an=1/[（2n+1）（2n-1）]

已知数列an满足a1=1/2 sn=n平方×an 求an 已知数列{an},满足a1=1/2,Sn=n²×an,求an 已知数列{an}a1=2前n项和为Sn 且满足Sn Sn-1=3an 求数列{an}的通项公式an 已知数列｛an｝满足an+1+an=4n-3 当a1=2时,求Sn 数列｛an｝满足a1=1,且an=an-1+3n-2,求an 已知数列{an}满足a1=1/2,sn=n^2an,求通项an 数列an满足sn=3an-1/2 计算a1,a2,a3,a4 猜an通项求an前n项和sn 已知数列an满足a1=1,a（n+1）=an/{3（an）+1} Sn=a1a2+a2a3+.+an（an+1）,求Sn 已知数列{an}满足a1=1,a(n+1)=3an+2,求数列{an}的前n项和Sn. 已知数列{an}满足an+1=2an+3.5^n,a1=6.求an 已知数列An的前n项和Sn满足An+2Sn*Sn-1=0,n大于等于2,A1=1/2,求An. 数列{an}满足a1=1,an=3n+2an-1(n≥2)求an