已知数列[an]满足Sn=0.25an+1,求a1+a3+a5+……+a2n-1的极限

来源：学生作业学帮网编辑：学帮网时间：2024/05/30 01:44:14

Sn=0.25an+1,
n=1时,a1=0.25a1+1,a1=4/3
n>1时,S（n-1）=0.25a（n-1）+1
两式相减,得an=0.25an-0.25a(n-1),an/a(n-1)=-1/3
an=4/3•(-1/3)^(n-1)
a1+a3+a5+……+a2n-1=4/3+4/3•1/9+4/3•1/81+……4/3•(1/9)^(n-1)
a1+a3+a5+……+a2n-1的极限=(4/3)/(1-1/9)=3/2

已知数列{an}满足:a1=3,an=Sn-1+2n,求数列an及sn 一个数列问题已知数列an前n项为sn,满足an+sn=2n.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=n^2an,求通项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Sn+an=2n+1.求an 已知数列{an}的前n项和sn满足sn=an^2+bn,求证{an}是等差数列已知数列{an}中a1=1,且满足an+an-1不等于0,Sn=1/6*(an+1)(an+2).(1)求通项an,并说明{an}是什么数列(2)求数列{an}的前n项和Sn 已知数列[an]满足Sn=0.25an+1,求a1+a3+a5+……+a2n-1的极限已知数列an满足a1=1 ,Sn=(n+1)*an/2,求通项的表达式. 已知数列{an}满足an=n/2的n次方,求Sn 已知数列{an}满足Sn=n2+2n+1,求通项公式{an} 已知数列{an}的前n项和为Sn,且满足Sn=2an-1(n属于正整数),求数列{an}的通项公式an 已知数列（an）的前n项和为Sn,满足an+Sn=2n,证明数列(an-2)为等比数列并求出an 已知数列{an}中,an>0,前n项和为Sn,且满足Sn=1/8(an+2)^2.求证数列{an}是等差数列. 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