已知数列{an},定义其平均数是Vn=(a1+a2+……+an)/n ,n∈N*.

已知数列{an},定义其平均数是Vn=(a1+a2+……+an)/n ,n∈N*.
（1）若数列{an}的平均数Vn=2n+1,求an
（2）若数列{an}是首项为1,公比为2的等比数列,其平均数为Vn,对任意的n∈N*,（Vn+1/n)*k>=3恒成立,求实数k的取值范围

(1)
Sn =a1+a2+..+an
Vn = 2n+1
Sn/n = 2n+1
Sn = n(2n+1) (1)
S(n-1) = (n-1)(2n-1) (2)
(1)-(2)
an = n(2n+1) -(n-1)(2n-1)
= 2n^2 +n -(2n^2-3n+1)
=4n-1
(2)
an = 2^(n-1)
Sn = a1+a2+..+an
= 2^n-1
Vn = (2^n-1)/n
(Vn + 1/n).k >=3
(2^n). k >=3
k >= 3. 2^(-n)