设各项均为正数的数列an的前n项和为sn,已知2a2=a1 a3

这是今年江苏卷上的题目…………(1)设根号Sn=d*n+HSn=d^2*n^2+2*d*H*n+H^2a1=S1=d^2+2*d*H+H^2a2=S2-S1=3*d^2+2*d*Ha3=S3-S2=5

1、√S1=√a1√S2=√(a1+a2)=√a1+2(1)√S3=√(a1+a2+a3)=√(3a2)=√a1+4(2)由(1)得a1+a2=a1+4√a1+4√a1=(a2-4)/4代入(2)√(

好像问题没写全吧

数列各项均为正,Sn>0.2√Sn是a(n+2)与an的等比中项,则(2√Sn)²=(an+2)an4Sn=an²+2ann=1时,4a1=4S1=a1²+2a1a1&#

2Sn=an+an^22Sn-1=an-1+an-1^2两式相减：2an=an^2+an-(an-1+an-1^2)an^2-an-(an-1+an-1^2)=0(an-(an-1+1))(an+an

(1)S[1]=a[1]=1/2(a[1]+1/a[1]),于是：a[1]=1=√1-√0S[2]=a[2]+1=1/2(a[2]+1/a[2]),于是：a[2]=√2-1,S[2]=√2S[3]=a

（1）若λ=1,则（S（n+1）+λ）an=（Sn+1）a（n+1）两边除以ana（n+1）得S（n+1）/a（n+1）+1/a（n+1）=Sn/an+1/an∴Sn/an+1/an,是常数列.Sn/

an+Sn=4a(n-1)+S(n-1)=4相减：an/a(n-1)=1/2等比数列n=1时a1+a1=4a1=2an=2^(2-n)bn=1/n²数学归纳法n=2时T2=5/4

(1)(an+2)/2=根号下2Sn所以8Sn=(an+2)^2n=1,S1=a1.8a1=(a1+2)^2,得a1=2n=2,8S2=(a2+2)^2,8(a1+a2)=(a2+2)^2,得a2=6

n=1时,S1=a1=1/2(a1+1/a1),a1=1.n=2时,S2=a1+a2=1+a2=1/2(a2+1/a2),a2=√2-1.n=3时,S3=a1+a2+a3=√2+a3=1/2(a3+1

1.n=1时,2a1=2S1=a1²+1-4a1²-2a1-3=0(a1+1)(a1-3)=0a1=-1(数列各项均为正,舍去)或a1=3n≥2时,2an=2Sn-2S(n-1)=

sn=(1/8)(an+2)²S(n-1)=(1/8)[a(n-1)+2]²an=Sn-S(n-1)=(1/8){(an+2)²-[a(n-1)+2]²}=(1

6Sn=an^2+3an+26S(n-1)=a(n-1)^2+3a(n-1)+26Sn-6S(n-1)=6an=an^2+3an+2-a(n-1)^2-3a(n-1)-26an=an^2+3an-a(

1)6Sn=An^2+3An+2因为S1=A1所以6A1=A1^2+3A1+2A1^2-3A1+2=0(A1-1)(A1-2)=0因为A1=S1>1所以A1=2因为An=Sn-S(n-1)注S(n-1

当n=1时,S1=a1=1/2(a1^2+a1),解得a1=1当n＞1时,an=Sn-S(n-1)=1/2(an^2+an)-1/2[a(n-1)^2+a(n-1)],整理得[an+a(n-1)][a

（1）a1＝(a1+1)24，解得a1=1，当n≥2时，由an=Sn-Sn-1=(an+1)2−(an−1+1)24，得（an-an-1-2）（an+an-1）=0，又an＞0，所以an-an-1=2

（1）当n=1时，a1＝s1＝14a21+12a1−34，解出a1=3，又4Sn=an2+2an-3①当n≥2时4sn-1=an-12+2an-1-3②①-②4an=an2-an-12+2（an-an

根号Sn的通项公式是nSn=n^2an=Sn-Sn-1=n^2-(n-1)^2=2n-1

Sn、an、1成等差,则2an=Sn＋1(n=1时,得a1=1),当n≥2时,有2a(n－1)=S(n－1)＋1,则2an－2a(n－1)=an,即an/[a(n－1)]=2=常数,所以{an}是等比