已知数列an是等比数列,前三项为a,1/2a+1/2,1/3a+1/3.数列前n项和为Sn,求lim Sn.

来源：学生作业帮编辑：拍题作业网作业帮分类：数学作业时间：2024/04/29 20:14:43

(1/2a+1/2)^2=a*(1/3a+1/3)
1/4(1/a+1)^2=1/3*a*(1/a+1)
1/4(1/a+1)=1/3*a
3(1/a+1)=4a
3(1+a)=4a^2
4a^2-3a-3=0
等比数列
[1/2(a+1)]^2=a*[1/3(a+1)]
1/4*(a+1)^2=a/3*(a+1)
等比数列的项不等于0
a+1不等于0
所以(a+1)/4=a/3
a=3
所以a1=3,a2=2,q=2/3
an=a1q^(n-1)
=3*(2/3)^(n-1)
Sn=3*[1-(2/3)^n]/(1-2/3)
=9*[1-(2/3)^n]
=9-9*(2/3)^n
lim Sn=9

已知数列an是等差数列,且a1≠0,Sn为这个数列的前n项和.求1、lim nan/Sn 2、lim (Sn+Sn+1) 已知数列 an前n项和为Sn,a1=1,Sn=2a(n+1),求Sn 等比数列的证明方式数列An的前n项和为Sn,A1=1,A(n+1)=2Sn+1,证明数列An是等比数列证明数列是等比数列数列前n项和为Sn,a1=1,a(n+1)=（n+2)Sn/n,求证Sn/n是等比数列, 已知数列an的前n项和为Sn,数列根号Sn+1是公比为2的等比数列已知数列an的前n项和为Sn,且Sn=（1/2)的n次方+a,若an为等比数列,则a=多少? 已知数列{An},Sn是其前n项和,且满足3An=2Sn+n,n为正整数,求证数列{An+1/2}为等比数列数列An的前n项和为Sn,已知A1=1,An+1=Sn*(n+2)/n,证明数列Sn/n是等比数列已知数列{An}是首项为a且公比q不等于1得等比数列,Sn是其前n项和,A1,2A7,3A4成等差数列. 已知数列an是首项为a 且公比q不等于一1的等比数列 sn是其前n项和 a1 2a7 3a4成等差数列已知数列an是首项为a且公比q不等于1的等比数列,Sn是其前n项和,a1,2a7,3a4成等差数列. 数列{an}前n项和为Sn,且an+Sn=-2n-1 证明{an+2}是等比数列