已知数列{an}的前n项和为Sn,Sn=(an-1)/3 (n∈N)(1)求a1,a2(2)求证数列{an}是等比数列
问题描述:
已知数列{an}的前n项和为Sn,Sn=(an-1)/3 (n∈N)
(1)求a1,a2
(2)求证数列{an}是等比数列
答
n=1,S1=a1=(a1-1)/3,a1=-1/2;n=2,S2=a1+a2=(a2-1)/3,a2=+1/4;an=Sn - Sn-1 =(an-1)/3 - (an-1 -1)/3=an/3- an-1/32an/3=-( an-1 /3); an/ an-1 = -1/2由a1=-1/2;a2=+1/4;以及an/ an-1 = -1/2(n∈N)知数列{an}...