已知数列{an},满足a1=1/2,Sn=n²×an,求an

来源：学生作业帮助网编辑：作业帮时间：2024/04/29 03:15:01

已知数列{an},满足a1=1/2,Sn=n²×an,求an
已知数列{an},满足a1=1/2,Sn=n²×an,求an

已知数列{an},满足a1=1/2,Sn=n²×an,求an

n≥2时,
Sn=n²×an S(n-1)=(n-1)²×a(n-1)
an=Sn-S(n-1)=n²×an-(n-1)²×a(n-1)
(n²-1)an-(n-1)²×a(n-1)=0
(n-1)[(n+1)an-(n-1)a(n-1)]=0
n≥2,n-1≥1,等式两边同除以n-1
(n+1)an-(n-1)a(n-1)=0
an/a(n-1)=(n-1)/(n+1)
a(n-1)/a(n-2)=(n-2)/n
…………
a2/a1=1/3
连乘
an/a1=(1/3)(2/4)...[(n-1)/(n+1)]=[1×2×...×(n-1)]/[3×4×...×(n+1)]=2/[n(n+1)]
an=2a1/[n(n+1)]=1/[n(n+1)]=1/n -1/(n+1)
n=1时,a1=1/1-1/2=1/2,同样满足通项公式
数列{an}的通项公式为an=1/n -1/(n+1).

可以求出 an=1/2n

已知数列{an}满足:a1=3,an=Sn-1+2n,求数列an及sn 已知数列{an}满足a1=1/2,sn=n^2an,求通项an 已知数列{an},满足a1=1/2,Sn=n²×an,求an 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=N²An 求An 已知数列an满足a1=1 Sn=2an+n 求an 已知数列an满足a1=1 ,Sn=(n+1)*an/2,求通项的表达式. 已知数列an的前n项和sn与通项an满足a1=2,sn+1sn=an+1,求sn 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}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a1=2,且2Sn+1Sn/(Sn-Sn+1)=1,求{an}通相公式已知数列{an}的前n项和为Sn,且满足an+2Sn*Sn-1=0,a1=1/2.求证：{1/Sn}是等差数列已知数列{an}满足a1=1,Sn=[(n+1)/2]*an,求通项an.急,思路也要已知数列｛an｝满足an+1+an=4n-3 当a1=2时,求Sn 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. 已知正数数列an满足a1=1 sn=1/2（an+1/an),其中sn为其前n项和,则sn=?请详解高数,已知数列An满足A1=1／2,且前n项和Sn满足Sn=n²An,则An=? 已知数列An满足A1=1／2,且前n项和Sn满足Sn=n²An,则An 已知数列{an}满足a1=1,an+1=2an+1.(1)求证:数列{an+1}是等比数列;(2)求an和Sn的表达式.