设数列an满足 a1=5/6,且an=1/3a(n-1)+1/3 求证 数列an-1/2为等比数列
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:2024/11/06 05:45:05
设数列an满足 a1=5/6,且an=1/3a(n-1)+1/3 求证 数列an-1/2为等比数列
并求an的通项公式与前n项和Sn
并求an的通项公式与前n项和Sn
an=(1/3)a(n-1)+1/3
an -1/2 = (1/3)[a(n-1) -1/2]
(an -1/2)/[a(n-1) -1/2] =1/3
=>{an-1/2}为等比数列
(an -1/2)/[a(n-1) -1/2] =1/3
(an -1/2)/[a1 -1/2] =(1/3)^(n-1)
an-1/2 = (1/3)^n
an = 1/2 + (1/3)^n
Sn =a1+a2+...+an
= n/2 + (1/2)(1-(1/3)^n)
an -1/2 = (1/3)[a(n-1) -1/2]
(an -1/2)/[a(n-1) -1/2] =1/3
=>{an-1/2}为等比数列
(an -1/2)/[a(n-1) -1/2] =1/3
(an -1/2)/[a1 -1/2] =(1/3)^(n-1)
an-1/2 = (1/3)^n
an = 1/2 + (1/3)^n
Sn =a1+a2+...+an
= n/2 + (1/2)(1-(1/3)^n)
设数列{an},a1=3,a(n+1)=3an -2 (1)求证:数列{an-1}为等比数列
已知数列{an}满足a1=1,a(n+1)=3an+2(n属于N) 1.求证数列{an+1}是等比数列 2.求{an}的
已知数列an满足an+1=3an+1,且a1=1/2,求证:数列{an+1/2}为等比数列
设数列{an},a1=3,前n项a(n+1)=3a-2 求证数列{(an)-1}为等比数列
数列{an}满足 a1=2,a2=5,an+2=3an+1-2an.(1)求证:数列{an+1-an}是等比数列; (2
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}满足a1=1,且an=an-1+3n-2,求an
已知数列{an}满足a1=1,an+1=2an+1 1)求证:数列{an+1}为等比数列; 2) 求{an}的通项an
已知数列{an}满足a1=1,a(n+1)=2an+1.求证(1)数列a(n+1)是等比数列;(2)求an
设数列{an}满足an+1/an=n+2/n+1,且a1=2
高中数列{An}前n项和Sn且A1=0 ,S(n+1)=4An+2.求证{A(n+1)-2An}为等比数列.
设数列An的前n项和为Sn,已知a1=1,An+1=Sn+3n+1求证数列{An+3}是等比数列