Question

数列{an}是首项为10,公比为10的等比数列,数列{bn}满足bn=1/n(lga1+lga2+...+lgan)n∈

Answer 1

An=10×10^(n-1)=10^n

lgAn=lg10^n=n

{lgAn}是等差数列

Bn=(lgA1+lgA2+……+lgAn)/n

=(1+2+……+n)/n

=[(1+n)n/2]/n

=(n+1)/2

B(n+1)-Bn=(n+2)/2-(n+1)/2=1/2

{Bn}是等差数列