已知an的前n项和sn=3n的平方 8n
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![已知an的前n项和sn=3n的平方 8n](/uploads/image/f/4216385-65-5.jpg?t=%E5%B7%B2%E7%9F%A5an%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8Csn%3D3n%E7%9A%84%E5%B9%B3%E6%96%B9+8n)
S1=A1=2A1-3故A1=3而An=Sn-S(n-1)=(2An-3n)-[2A(n-1)-3(n-1)]=2An-2A(n-1)-3故An=2A(n-1)+3故An+3=2[A(n-1)+3]即
Sn=2An-3nS(n-1)=2A(n-1)-3(n-1)两式相减An=2An-3n-(2A(n-1)-3(n-1))An=2A(n-1)-3所以An是等差数列(An-3)/((An-1)-3)=2
n=1,S1=a1=(a1-1)/3,a1=-1/2;n=2,S2=a1+a2=(a2-1)/3,a2=+1/4;an=Sn-Sn-1=(an-1)/3-(an-1-1)/3=an/3-an-1/32
an看做两个数列,其中n^2求和根据平方数列求和公式为:n(n+1)(2n+1)/6n求和根据等差数列求和公式为:(1+n)*n/2两者相加即为答案
an=sn-Sn-1(1)Sn=3n^2-nSn-1=3(n-1)^2-(n-1)Sn-Sn-1=3(2n-1)-1=6n-4
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
(1)当n=1时a(1)=S(1)=3-5/2=1/2当n≥2时a(n)=S(n)-S(n-1)=3n^2-5n/2-3(n-1)^2+5(n-1)/2=6n-11/2其中n=1是也符合上式,所以a(
(1)如果an=n,bn=(1/3)*n,则an/bn=3,因此Sn=3n;(2)如果an=n,bn=1/(3n),那么an/bn=3n^2,因此Sn=n(n+1)(2n+1)/2.(有公式1^2+2
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-
an=Sn-Sn-1=1/3n(n+1)(n+2)-1/3n(n+1)(n-1)=n(n+1)所以1/an=1/n(n+1)=1/n-1/n+1数列(1/an)的前n项和=1-1/2+1/2-1/3+
Sn=3+2^nSn-1=3+2^n-1an=sn-sn-1=3+2^n-3-2^(n-1)=2^n-2^(n-1)=2*2^(n-1)-2^(n-1)=2^(n-1)
(1)令n=1a1=S1=32-1+1=32Sn=32n-n²+1Sn-1=32(n-1)-(n-1)²+1an=Sn-Sn-1=32n-n²+1-32(n-1)+(n-
(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{
A(n+1)=S(n+1)-Sn=2(n+1)^2+3(n+1)+2-2n^2-3n-2=2n^2+4n+2+3n+3-2n^2-3n=4n+5An=5+4(n-1)
【方法1:强行展开a(n)表达式】1+2+……+n=n(n+1)/21^2+2^2+……+n^2=n(n+1)(2n+1)/61^3+2^3+……+n^3=n^2(n+1)^2/41^4+2^4+……
Sn+an=n^2+3n+5/2①当n=1时,S1+a1=1^2+3*1+5/2=13/2而S1=a1,所以2a1=13/2,即a1=13/4,所以a1-1=9/4;又S(n-1)+a(n-1)=(n
不是这样的1、A(n+1)=S(n+1)-Sn=Sn+3^n>>>>S(n+1)-3^(n+1)=2Sn+3^n-3^(n+1)=2Sn-2×3^n=2[Sn-3^n]则:[S(n+1)-3^(n+1
n=k,a1/1^2+a2/2^2+a3/3^2.+ak/k^2>3^kn=k+1,a1/1^2+a2/2^2+a3/3^2.+ak/k^2+a(k+1)/(k+1)^2>3^k+a(k+1)/(k+
Sn=3an+2n可得S(n-1)=3a(n-1)+2n-2an=Sn-S(n-1)=3an+2n-3a(n-1)-2n+2即:an=3an-3a(n-1)+23a(n-1)=2an+2配项可得:3[
看不懂啊是Sn=2n^2-(3n+1)还是Sn=(2n)^2-(3n+1)?题目容易令n=1求出a1=-2Sn-1=2(n-1)^2-3(3(n-1)+1)an=Sn-Sn-1=2(2n-1)-3=4