s2n-1等于什么
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解题思路:数列性质解题过程:,
因为数列{an}为等差数列,且a1=1,则由等差数列性质可得:前n项和Sn=a1n-(n(n-1)/2)*D即Sn=n-(n(n-1)/2)*D,S2n=2n-(2n(2n-1)/2)*D且S2n/S
分子分母同时乘以i,得i/i,因为i=-1,所以答案为-i.
S2n表示的是前2n项的和,不是原Sn的每2项为一组的新序列的和;(1-1/n)^-n.
Sn=n的平方,S2n=4倍的n平方!limSn/S2n=lim(n的平方)/(4倍的n平方)=1/4
2
Sn,S2n-Sn,S3n-S2n.仍成等比数列
(1)Sn=48=a1+a2+……+an=48S2n=a1+a2+……an+a(n+1)+……a(2n)=60Sn+Sn*q^n=S2nq^n=1/4S3n=a1+……a(3n)=S2n+a(2n+1
①依题意知sns2n-sns3n-s2n成等比数列设s3n=x那么有48*(x-60)=(60-x)^2解出x即可②在原式两边同时减去2得an-1=2a(n-1)-2即an-1/[a(n-1)-1]=
Sn=a1(1-q^n)/1-q=48s2n=a1(1-q^2n)/1-q=60那么s2n/sn=1+q^n=60/48q^n=1/4q^2n=1/16q^3n=1/64s3n=a1(1-q^3n)/
等比数列的Sn,S2n-Sn,S3n-S2n也成等比数列.即48,12,S3n-60成等比S3n-60=12^2/48=3s3n=63
Sn,S2n,S3n,成等差数列,2*S2n=Sn+S3nS3n=72补充,像S1,Sk,S2k,S3k,下标成等差数列,则这三个数成等差数列再问:已知等差数列{an}中,a3=-2,a8=8,求a1
等于8
10
利用等比数列的性质可得,a1a2a3=a23=8 即a2=2因为S2n=3(a1+a3+…+a2n-1)所以n=1时有,S2=a1+a2=3a1从而可得a1=1,q=2所以,a10=1×29
3呗
S2n=1+1/2+1/3+...+1/n+1/(n+1)+1/(n+2)+...+1/(2n)Sn=1+1/2+.+1/n令Tn=S2n-Sn则Tn=1/(n+1)+1/(n+2)+1/(n+3)+
n是奇数,是个等差数列ak的后一项是a(k+2)所以公差是4,最后一项是a(2n-1)=4n-1a1=3,有n项所以和=(3+4n-1)*n/2=2n^2+nn是偶数同理,ak的后一项是a(k+2)所
S2n=2n+n*(2n-1)dSn=n+n(n-1)d/24Sn=4n+2(n^2-n)dS2n/Sn=4S2n=4Sn4n+2d(n^2-n)=2n+(2n^2-n)d整理,得dn=2nd=2S2