已知无穷等比数列{An}的首项A1＝－1,前n项和为Sn,若S10/S5=31/32,则lim＝应该是limSn=

Question

已知无穷等比数列{An}的首项A1＝－1,前n项和为Sn,若S10/S5=31/32,则lim＝_________
应该是limSn=

Answer 1

等比数列前n项和为Sn=A1(1-q^n)/(1-q)
S10=A1(1-q^10)/(1-q)=A1(1-q^5)(1+q^5)/(1-q)
S5=A1(1-q^5)/(1-q)
S10/S5=1+q^5=31/32
∴q^5=-1/32
q=-1/2
∴limSn=A1/(1-q)=-1/(1+1/2)=-2/3