设等差数列an的前n项和为Sn,已知bn=1/Sn,且a3*b3=1/2,S3+S5=21,求bn,bn前n项和Tn.

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/24 18:54:21
设等差数列an的前n项和为Sn,已知bn=1/Sn,且a3*b3=1/2,S3+S5=21,求bn,bn前n项和Tn.设等差数列an的前n项和为Sn,已知bn=1/Sn,且a3*b3=1/2,S3+S

设等差数列an的前n项和为Sn,已知bn=1/Sn,且a3*b3=1/2,S3+S5=21,求bn,bn前n项和Tn.
设等差数列an的前n项和为Sn,已知bn=1/Sn,且a3*b3=1/2,S3+S5=21,求bn,bn前n项和Tn.

设等差数列an的前n项和为Sn,已知bn=1/Sn,且a3*b3=1/2,S3+S5=21,求bn,bn前n项和Tn.
S3=3a1+3*2*d/2=3a1+3d
s5=5a1+5*4*d/2=5a1+10d
a3*b3=(a1+2d)/S3=(a1+2d)/(3a1+3d)
S3+S5=3a1+3d+5a1+10d=8a1+13d
(a1+2d)/(3a1+3d)=1/2
8a1+13d=21
解得,a1=1,d=1
Sn=na1+n(n-1)d/2=n(n+1)/2
bn=1/[n(n+1)/2]=2/[n(n+1)]
Tn=2/(1*2)+2/(2*3)+...+2/[n(n+1)]
=2*[1-1/2+1/2-1/3+...+1/n-1/(n+1)]
=2*[1-1/(n+1)]
=2n/(n+1)

已知数列an的前n项和为sn=5/6n(n+3),1:求证an为等差数列 2:设bn=a3n+an+1 已知等差数列{an}的前n项和为Sn,且a2=1,S11=33,设bn=(1/2)^an,证明{bn}为等比数列 已知an是首项为19,公差为-2,的等差数列,sn为an的前n项和 1.求通项an及sn 2.设(已知an是首项为19,公差为-2,的等差数列,sn为an的前n项和1.求通项an及sn2.设(bn-an)是首项为1,公比为3的等比例,求数列bn的 (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 设数列【An】的前n项和为Sn,A1=10,An+1=9Sn+10.设Bn=lgAn,求证数列【Bn】为等差数列 设等差数列an的前n项和为Sn,已知bn=1/Sn,且a3*b3=1/2,S3+S5=21,求bn,bn前n项和Tn. 已知Sn为等差数列An的前n项和,Bn=Sn/n(n属于正整数),求证:数列Bn是等差数列 已知等差数列{an}的前3项和为6,前8项和为-4设bn=(4-an)q^(n-1) (q不等于0,n属于正整数)求数列{bn}的前n项和Sn 已知等差数列(an)的前n项和为Sn,且a3=5,S15=225,设bn=2^a n+2n,求数已知等差数列(an)的前n项和为Sn,且a3=5,S15=225,设bn=2^a n+2n,求数列{bn}的前n项和Tn 设等差数列an的前n项和为sn,已知a6=13,S10=120,设bn=sn/(n+c),且数列bn是等差数列,求非零常数c的值. 已知数列 an 的前n项和为sn,满足an+Sn=3-8/2的n次方设bn=2的n次方乘an求证;数列bn是等差数列 等差数列{an}的前n项和为Sn,S4=-62,S6=-75,设bn=|an|,求数列{bn}的前n项和Tn. 已知两个等差数列{an},{bn}的前n项的和分别为Sn,Tn.若Sn/Tn=(5n+3)/(2n-1).求an/bn 已知等差数列an,bn,的前n项和分别为Sn,Tn,若Sn/Tn=2n/3n+1,求an/bn, 关于等差数列的题设数列{An}的前n项和为Sn,已知A1=1,且满足3Sn^2=An(3Sn-1)(n≥2)(1)求证:数列{1/Sn}是等差数列(2)设bn=Sn/3n+1,求数列{bn)的前n项和n 已知a1,a2,a3,…,an成一个等差数列,其前n项和为Sn=n^2,设bn=an/3^n,记{bn}的前n项和为Tn 证明 Tn 已知{an}是等差数列,记bn=anan+1an+2(n∈N*),设Sn为{bn}的前n项和,且3a5=8a12>0,则当Sn取最大值时,n= 已知等差数列{an}的前n项和为Sn,如果Sn=(an+1/2)^2(n∈N+0,bn=(-1)^n*Sn已知等差数列{an}的前n项和Sn,如果Sn=(an+1/2)^2(n∈N+0,bn=(-1)^n*Sn,试求{bn}的前n项和Tn