已知等差数列{an}的前n项和是sn=32n一n*n,求{|an|}的前n项和sn

来源：学生作业帮助网编辑：作业帮时间：2024/05/04 15:33:12

已知等差数列{an}的前n项和是sn=32n一n*n,求{|an|}的前n项和sn
已知等差数列{an}的前n项和是sn=32n一n*n,求{|an|}的前n项和sn

已知等差数列{an}的前n项和是sn=32n一n*n,求{|an|}的前n项和sn
当n=1时
a1=s1=32*1-1*1=31
当n≥2时
an=Sn-S(n-1)
=32n-n²-[32(n-1)-(n-1)²]
=32n-n²-(32n-32-n²+2n-1)
=-2n+33
令an>0,则-2n+33>0
解得：n

全部展开

是这样的吗:Sn=32n-n^2:
a1=S1=32-1=31
n>=2:an=Sn-S[n-1]=32n-n^2-32(n-1)+(n-1)^2=32-2n+1=33-2n
an<0,有n>33/2,即有当a16>0,a17<0
{|an|}的前n项和Sn
(1)n<=16,Sn=(a1+an)n/2=(31+33-2n)n/2=32n-n^2
n>17,Sn=(a1+...+a16)-(a17+a18+...+an)
=-(a1+...+a16+a17+...+an)+2(a1+...+a16)
=-(32n-n^2)+2(31+1)*16/2
=n^2-32n+256

收起

已知an是等差数列,前n项和为Sn,求证:S3n=3(S2n-Sn) 已知数列{an}的前n项和为Sn=n^2-3n,求证：数列{an}是等差数列已知数列｛an｝的前n项和sn=n方+3n,求证数列{an}是等差数列 (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Sn=4n2+3n,求证{An}是等差数列已知数列{an}的前n项和sn满足sn=an^2+bn,求证{an}是等差数列已知sn=32n-n^2求等差数列|an|的前n项和sn 已知等差数列{an}的前n项和是sn=32n一n*n,求{|an|}的前n项和sn 已知数列{an}的前n项和Sn=100n-n^2,证明{an}是等差数列已知等差数列{an}前n项和Sn=-2n2-N,求通项an的表达式已知等差数列{an}的前n项和Sn=n²求an {an}是等差数列前n项和Sn已知Sm=a Sn-Sn-m=b 求Sn 已知公差不为0的等差数列{An}的首项A1=1,前n项和为Sn,若数列{Sn/An}是等差数列,求An? 已知数列{an}的前n项和为Sn,且满足an+2Sn*Sn-1=0,a1=1/2.求证：{1/Sn}是等差数列已知数列{an}的前n项和Sn=2n方-3n 1.求{an}的通项公式 2.证明{an}是等差数列已知数列{An}的前n项和Sn=3n²-2n,证明数列{An}为等差数列已知一等差数列{an}的前n项和Sn=n^2-3n+1,求an 已知等差数列的前n项和An=n^2-17n.即便Sn最小的n值是