某数列的前n项和为Sn,不等式an^2 Sn^2 n^2大于等于ma1^2
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1、Sn=(a1+an)n/2所以nan/Sn=2an/(a1+an)=2[a1+(n-1)d]/[2a1+(n-1)d]上下除以(n-1)=2[a1/(n-1)+d]/[2a1/(n-1)+d]n-
Sn=n-5an-85(1)S(n+1)=n+1-5a(n+1)-85(2)(2)-(1)整理得6a(n+1)=1+5an即a(n+1)-1=(5/6)(an-1)又由S1=a1=1-5a1-85得a
证:(1)根号Sn+1=(a1+1)*2^(n-1)=4*2^(n-1)=2^(n+1)Sn+1=2^(2n+2)=4^(n+1).1Sn=4^n.21式-2式Sn+1-Sn=4^(n+1)-4^na
由Sn=n-Sa知,an=Sn-Sn-1=1(>=2).a1=1-Sa
1.n=1时,a1=S1=1²+1=2n≥2时,Sn=n²+nS(n-1)=(n-1)²+(n-1)an=Sn-S(n-1)=n²+n-(n-1)²-
Sn=(n^2+n)/21/Sn=1/((n2+n)/2)=2/(n^2+n)Tn=1+2/6+2/12+2/30+.+2/n*(n+1)=1+(2/2-2/3)+(2/3+2/4)+.+(2/n-2
(1)当n=1时,a1=S1=lg1=0(2)当n>=2时,an=Sn-Sn-1=lgn-lg(n-1)=lg(n/(n-1))所以,a1=0;an=lg(n/(n-1))(n>=2)(可把结果写成分
为了避免混淆,我把下角标放在内.首先从数列本身的基本意义出发a=S-S其次,从已知a=S(n+2)/n出发a=S*(n+1)/(n-1)因此S-S=S*(n+1)/(n-1)移项整理S=S
(1)证明:∵Sn=n-5an-85,n∈N*(1)∴Sn+1=(n+1)-5an+1-85(2),由(2)-(1)可得:an+1=1-5(an+1-an),即:an+1-1=56(an-1),从而{
S1=a1=1-1*a12a1=1a1=1/2S2=1-2a2=a1+a2=1/2+a23a2=1/2a2=1/6Sn=1-nanSn-1=1-(n-1)a(n-1)相减an=Sn-Sn-1=1-na
1/n(n+1)=[(n+1)-n]/n(n+1)=1/n-1/(n+1)所以Sn=1-1/2+1/2-1/3+……+1/n-1/(n+1)=1-1/(n+1)所以S2009=1-1/2010=200
(1)当n=1时,a1=S1=13(a1−1),得a1=−12;当n=2时,S2=a1+a2=13(a2−1),得a2=14,同理可得a3=−18.(2)当n≥2时,an=Sn−Sn−1=13(an−
设数列{an}的前n项和为Sn,Sn=a1(3n−1)2(对于所有n≥1),则a4=S4-S3=a1(81−1)2−a1(27−1)2=27a1,且a4=54,则a1=2故答案为2
∵数列1,11+2,11+2+3,…∴an=2n(n+1)=2(1n−1n+1)Sn=a1+a2+…+an=2(1-12+12-13+…1n-1n+1)=2(1-1n+1)=2nn+1故答案为:2nn
你那样求,很明显是错误的.Sn是2^n*An的前n项和,所以必须按照下面的方法求2^n*An的前n项和为Sn=9-6nSn-S(n-1)=(9-6n)-(9-6(n-1)=9-6n-9+6n-6=-6
∵数列{an}的前n项和为Sn,Sn=1-23an,∴a1=s1=1-23a1,解得 a1=35.且n≥2时,an=Sn-Sn-1=(1-23an)-(1-23an-1)=23an-1-23
解题思路:方法:数列通项的求法:已知sn,求an。求和:错位相减法。解题过程:
(1)当n=1时,T1=2S1-1因为T1=S1=a1,所以a1=2a1-1,求得a1=1(2)当n≥2时,Sn=Tn-Tn-1=2Sn-n2-[2Sn-1-(n-1)2]=2Sn-2Sn-1-2n+
S(n+1)=2Sn+n+1所以Sn=2S(n-1)+n两个式子相减所以a(n+1)=2an+1a(n+1)+1=2an+2a(n+1)+1=2(an+1)所以an+1是等比数列,公比为2首项=a1+
解题思路:考查数列的通项,考查等差数列的证明,考查数列的求和,考查存在性问题的探究,考查分离参数法的运用解题过程: