前n项和Sn=2^n-1
an=Sn-Sn-1
an=2^n-1-2^(n-1)+1
an=2^(n-1)
(an)^2÷(an-1)^2=2^(2n-2) ÷ 2^(2n-4)
(an)^2÷(an-1)^2=4
则(an)^2为公比为4的等比数列
(a1)^2=1
则(an)^2=4^(n-1)
数列的和为(4^n-1)/3