已知数列an的前n项和为Sn,且满足an=6Sn-2已知数列｛an｝的前n项和为Sn,且满足an=6Sn-2,（n∈N）（1）求数列｛an｝的通项公式（2）求lim(n→∞）Sn过程~~~~~~~~~~~~~~~

Question

已知数列an的前n项和为Sn,且满足an=6Sn-2
已知数列｛an｝的前n项和为Sn,且满足an=6Sn-2,（n∈N）
（1）求数列｛an｝的通项公式
（2）求lim(n→∞）Sn
过程~~~~~~~~~~~~~~~

Answer 1

(1)
an=6Sn-2 (1)
put n=1
5a1=2
a1=2/5
a(n-1) = 6S(n-1) -2 (2)
(1)-(2)
an-a(n-1) = 6an
an/a(n-1) = -1/5
an/a1 = (-1/5)^(n-1)
an = (2/5).(-1/5)^(n-1)
= (-2)(-1/5)^n
Sn = (2/5)( 1- (-1/5)^n)/ (1+1/5)
=(1/3)( 1- (-1/5)^n)
lim(n→∞）Sn = 1/3