已知在正项数列an中sn表示前n项和且2倍根号下sn=an 1
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![已知在正项数列an中sn表示前n项和且2倍根号下sn=an 1](/uploads/image/f/4258046-38-6.jpg?t=%E5%B7%B2%E7%9F%A5%E5%9C%A8%E6%AD%A3%E9%A1%B9%E6%95%B0%E5%88%97an%E4%B8%ADsn%E8%A1%A8%E7%A4%BA%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%942%E5%80%8D%E6%A0%B9%E5%8F%B7%E4%B8%8Bsn%3Dan+1)
数列{a(n)}中,已知s(n)=a(n)-1/s(n)-2,①:求出s(1),s(2),s(3),s(4),②:猜想数列{a(n)}的前n项和s(n)的公式,并加以证明s(1)=a(1)=a(1)-
a1+a2=2*1-1+3*2+2=9a(n-1)+an=2*(2-1)-1+3n+2=5n-1等差a9+a10=49S10=(9+49)*5/2=145S15=S14+a15Sn同理可求
(1)数列{an}中,a1=1,前n项和Sn=n+23an,可知S2=43a2,得3(a1+a2)=4a2,解得a2=3a1=3,由S3=53a3,得3(a1+a2+a3)=5a3,解得a3=32(a
(1)Sn=(an+1)^2/4a1=S1=(a1+1)^2/4a1=14Sn=an^2+2an+14S(n-1)=a(n-1)^2+2a(n-1)+14an=(an+a(n-1))(an-a(n-1
由题意得,Sn=[(an+1)/2]^2①则S(n+1)=[(a(n+1)+1)/2]^2②②-①得(结合a(n+1)=S(n+1)-Sn)a(n+1)=[(a(n+1)+1)/2]^2-[(an+1
设公比为q,当q=-1时,等比数列{an}的各项是a,-a,a,-a,a,-a…的形式,a≠0.又已知Sn是实数等比数列{an}前n项和,故当n为偶数时,Sn=0,当n为奇数时,Sn=a,故选D.
由题意得,Sn=[(an+1)/2]^2①则S(n+1)=[(a(n+1)+1)/2]^2②②-①得(结合a(n+1)=S(n+1)-Sn)a(n+1)=[(a(n+1)+1)/2]^2-[(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[3]
a3+a9=2a6a3+a6+a9=273a6=27a6=9s11=(a1+a11)x11/2=2a6x11/2=11a6=11x9=99
17.(1)因为Sn+1-Sn=an+1又因为Sn+1=Sn+2an所以an+1=2anan+1/an=2所以数列an为公比为2的等比数列a1=1an=a1q^(n-1)=2^(n-1)(2)没看懂.
Sn=3Sn-1Sn-1=3Sn-2(n>=3)相减后:an=3an-1等比数列q=an/an-1=3所以an=a2*3^n-2(n>=3)S2=3S1即a2+a1=3a1,故a2=2a1这样通项公式
a(n+1)=3a(n)/[a(n)+3],若a(n+1)=0,则,a(n)=0,...,a(1)=0,与a(1)=1/2矛盾.因此,a(n)不为0.1/a(n+1)=(1/3)[a(n)+3]/a(
a1=Sna1=S1=2an=Sn-Sn-1=n²+n-(n-1)²-(n-1)=2nan=2na2=2*2=4a3=2*3=6a1=2,a2=4,a3a=6an=2n
∵2根号Sn=an+14Sn=(an+1)^2①4S(n-1)=[a(n-1)]^2②①-②,可得:4an=[an^2-a(n-1)^2]+2[an-a(n-1)]化简可得:2[a(n-1)+an]=
∵Sn=3+2an,①∴Sn+1=3+2an+1,②②-①得Sn+1-Sn=2an+1-2an,即an+1=2an+1-2an, 移向整理得出an+1=2an, 又n=1时,a1=
设等差数列{an}的首项为公差为dSn=a1+a2+……+anS2n-Sn=an+1+an+2+……+a2nS3n-S2n=a2n+1+a2n+2+……+a3n(S2n-Sn)-Sn=(an-a1)+
sn=n^2ans(n-1)=(n-1)^2*a(n-1)sn-s(n-1)=n^2an-(n-1)^2*a(n-1)=an(n^2-1)an=(n-1)^2a(n-1)(n+1)an=(n-1)a(
n=1时,a1=S1=k+2n≥2时,Sn=2n²+kS(n-1)=2(n-1)²+kan=Sn-S(n-1)=2n²+k-2(n-1)²-k=4n-2数列{a
an=2S(n-1)an+S(n-1)=3S(n-1)Sn=3S(n-1)Sn/S(n-1)=3Sn是等比数列Sn/S(n-1)=3Sn/S1=3^(n-1)Sn=3^(n-1)(1)an=2S(n-