数列an,bn满足an>0,bn=1/n(log2a1+log2a2+…log2an)
问题描述：
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
答
(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
nmax Sn = S19 or S20
= (1/2+19/2)20/2
=100(1/n)log(a1.a2...an) 不该是 (1/n)log(a1+a2...+an)那个 “.” 是什么意思loga + logb=log(a.b)