等比数列{an}的公比为-1/2,前n项和Sn,满足limSn=1/a1,则首项a1

等比数列{an}的公比为-1/2,前n项和Sn,满足limSn=1/a1,则首项a1
等比数列{an}的公比为-1/2,前n项和Sn,满足limSn=1/a1,则首项a1

等比数列{an}的公比为-1/2,前n项和Sn,满足limSn=1/a1,则首项a1
由题意知该数列前n项和为：
Sn＝a1(1-q^n)/(1-q)
因为q=-1/2,limn->+∞ Sn=1/a1
所以lim(n->+∞) Sn
=lim(n->+∞) a1(1-q^n)/(1-q)
=a1/(1+1/2)
=1/a1
则(a1)²=3/2
解得a1=√6/2或a1=-√6/2