数列an,bn满足an>0,bn=1/n(log2a1+log2a2+…log2an)若{an}是等比数列,求证:{bn}是等差数列若{an}是以a1=1024为首项,公比q=1/2的等比数列,则n为何值时,数列bn的前n项和sn最大?并求最大值bn是n分之1

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/07 20:38:23

数列an,bn满足an>0,bn=1/n(log2a1+log2a2+…log2an)若{an}是等比数列,求证:{bn}是等差数列若{an}是以a1=1024为首项,公比q=1/2的等比数列,则n为何值时,数列bn的前n项和sn最大?并求最大值bn是n分之1
数列an,bn满足an>0,bn=1/n(log2a1+log2a2+…log2an)
若{an}是等比数列,求证:{bn}是等差数列
若{an}是以a1=1024为首项,公比q=1/2的等比数列,则n为何值时,数列bn的前n项和sn最大?并求最大值
bn是n分之1去乘以(log2a1+……log2an)
2是log的下角标,a1……an项都是直接跟在log后面的,不是下角标

数列an,bn满足an>0,bn=1/n(log2a1+log2a2+…log2an)若{an}是等比数列,求证:{bn}是等差数列若{an}是以a1=1024为首项,公比q=1/2的等比数列,则n为何值时,数列bn的前n项和sn最大?并求最大值bn是n分之1
(1)
an = a1q^(n-1)
bn=(1/n)(loga1+loga2+…+logan)
= (1/n)log(a1.a2...an)
=(1/n)log[(a1)^n .q^(n^2/2)]
=log [ a1.q^(n/2) ]
b(n+1) -bn = log [ a1.q^((n+1)/2) ] - log [ a1.q^(n/2) ]
= log q^(1/2)
{bn} 是等差数列
(2)
bn =log [ a1.q^(n/2) ]
=log [ 1024.(1/2)^(n/2) ]
=log [ 2^((20-n)/2) ]
= (20-n)/2
bn > 0
20-n >0
n< 20
max Sn = S19 or S20
= (1/2+19/2)20/2
=100

数列{an}与{bn}满足an=1/n(b1+b2+…+bn)(n∈N).求证:数列{bn}为等差数列的充要条件是数列{an}为等差数列 19、已知数列{an},{bn}满足a1=2,2a n=1+a na n+1,bn=an-1(bn不等于0)求证:数列{1/bn}是等差数列,并求数列{an}的通项公式. an=2*3^n-1 若数列bn满足bn=an+(-1)^n*ln(an),求数列bn前n项和Sn 正整数列{an},{bn}满足对任意正整数n,an、bn、an+1成等差数列,bn、an+1、bn+1成等比数列,证明:数列{根号bn}成等差数列 设数列{an},{bn}满足a1=1,b1=0且(高二数学,a(n+1)=2an+3bn且b(n+1)=an+2bn.(1)求证:{an+根号3bn}和{an-根号3bn}都是等比数列并求其公比;(2)求{an},{bn}的通项公式(n均为正整数)是(根号3)bn 已知数列满足an+1-an=2(n属于N*),且a9=17数列{bn}中,bn=3^an,求证数列{bn}是等比数列并...已知数列满足an+1-an=2(n属于N*),且a9=17数列{bn}中,bn=3^an,求证数列{bn}是等比数列并求其前n项和sn 已知数列{an}满足a1=4,a(n+1)an+6a(n+1)-4an-8=0,记bn=6/an-2,n属于N*(1)求数列{bn}通项公式已知数列{an}满足a1=4,a(n+1)an+6a(n+1)-4an-8=0,记bn=6/an-2,n属于N*(1)求数列{bn}通项公式(2)求数列{an·bn 数列{an} {bn}满足:a1=0 a2=1 a(n+2)=[an+a(n+1)]/2 bn=a(n+1)-an 求证 bn是等比数列和 bn的通向公式 已知an=2n-1,数列{bn}满足:b1/2+b2/2^2+...+bn/2^n=an,求数列{bn}的前n项和Sn 设数列{an},{bn}满足;a1=4 a2=5/2,an+1=an+bn/2,bn+1=2anbn/an+bn 用数列an表示an+1;并证明;任意n属于设数列{an},{bn}满足;a1=4 a2=5/2,an+1=an+bn/2,bn+1=2anbn/an+bn (1)用数列an表示an+1;并证明;任意n属于N*都 数列an的前n项和为Sn=2^n-1,设bn满足bn=an+1/an,判断并证明bn 的单调性 已知数列an满足an>0,Sn=[(an+1)/2]^2,bn=(-1)^n*Sn,求b1+b2+……+bn 18、一道数列题已求出数列An=2n.若数列Bn满足B(n+1)=Bn^2-(n-2)Bn+3,Bn大于等于1,证明:Bn大于等于An/2 已知数列an满足an=31-6n,数列bn满足bn=(a1+a2+...+an)/n,求数列bn的前20项之和. 数列{an}的前n项和为Sn,a1=1 an+1-an*1=0,数列{bn}满足b1=2,anbn+1=2an+1bn求 s200 求bn 已知在直角坐标系中,An(an,0),Bn(0,bn)(n∈N*),其中数列{an},{bn}都是递增数列……已知在直角坐标系中,An(an,0),Bn(0,bn)(n∈N*),其中数列{an},{bn}都是递增数列.(1)若an=2n+1,bn=3n+1,判断直线A1B1与A2B2是否 已知各项均为正数的两个数列an,bn满足a n+1=an+bn/√an²+bn² 数列{an}中,a1=-1,a2=0,a(n+1)+4a(n-1)=4an(n>=2),数列bn满足 bn=a(n+1)-2an (1)证数列bn为等比数列,并求数列an,bn的通项公式(2)求数列an的前n项和sn在线等.谢谢了