已知数列an的前N项和为Sn,Sn=2n^2+n,数列bn满足an=4LOG2bn+3,求an.bn的前N项和Tn

来源：学生作业帮助网编辑：作业帮时间：2024/11/08 09:00:37

已知数列an的前N项和为Sn,Sn=2n^2+n,数列bn满足an=4LOG2bn+3,求an.bn的前N项和Tn
已知数列an的前N项和为Sn,Sn=2n^2+n,数列bn满足an=4LOG2bn+3,求an.bn的前N项和Tn

已知数列an的前N项和为Sn,Sn=2n^2+n,数列bn满足an=4LOG2bn+3,求an.bn的前N项和Tn
Sn=2n^2+n
n=1, a1=3
an =Sn-S(n-1)
=2(2n-1) +1
=4n-1
an = 4log<2>bn +3
bn = 2^(n-1)
let
S =1.2^0+2.2^1+.+n.2^(n-1) (1)
2S = 1.2^1+2.2^2+.+n.2^n (2)
(2)-(1)
S=n.2^n-[1+2+...+2^(n-1)]
= n.2^n - (2^n-1)
cn=an.bn
=(4n-1).2^(n-1)
=4(n.2^(n-1)) - 2^(n-1)
Tn =c1+c2+...+cn
=4S - (2^n -1)
=4n.2^n -5(2^n -1)
=5 +(4n-5).2^n

已知数列{an}的前n项和为Sn,an+Sn=2,（n 已知数列an的前n项和为Sn,且An=3^n+2n,则Sn等于数列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 1.已知数列an的前n项和为Sn,且Sn=2^n,求通项an；2.已知数列an的前n项和为Sn,且Sn=n^2+3n,求通项an；已知数列an的前n项和为sn 若sn=2n-an,求an 一道关于数列已知数列{An}的前n项和为Sn,Sn=3+2An,求An 已知数列{an}的前n项和为Sn,若a1=1/2,Sn=n^2an-n(n-1)求Sn,an 已知数列{an}的前n项和为Sn=-n2-2n,求an 已知:sn为数列{an}的前n项和,sn=n^2+1,求通项公式an. 已知数列an的通向公式是an=|21-2n|,Sn为前n项和,求Sn (1)已知数列an的前n项和为sn满足sn=an²+bn,求证an是等差数列(2)已知等差数列an的前n项和为sn,求证数列sn/n也成等差数列已知数列{an}的前n项和为Sn,且Sn=2an-n（n∈N*）,求数列{an}的通项公式. 已知数列an的前n项和为sn,且sn+an=n^2+3n+5/2,证明数列{an-n}是等比数列数列｛an｝的前n项和记为sn,已知a1=1,an+1=((n+2)/n)sn(n∈n+),证明：(1)数列｛sn/n｝是等比数列；(2)sn+1=4an 详细已知数列an的前n项和为sn sn=3(的n次方)+1求数列an 已知数列 an前n项和为Sn,a1=1,Sn=2a(n+1),求Sn 已知数列前n项和为Sn,且Sn=-2n+3,求an及Sn 已知数列{an}的前n项和为Sn=n^2-3n,求证：数列{an}是等差数列