数列｛an｝的前n项和为Sn,已知an=5Sn-3,求（a1+a3+a5+...+a2n-1)的极限值.

a1=5a1-3,a1=3/4
an=5Sn-3
a(n-1)=5S(n-1)-3
an-a(n-1)=5Sn-5S(n-1)-3+3=5an
a(n-1)=4an
an为公比为1/4的等比数列
a(2n-1)为公比为1/16的等比数列
lim(a1+a3+a5+...+a2n-1)
=lim(a1(1-1/16^n)/(1-1/16))
=lim(16a1/15)
=16/15*3/4
=4/5