等比数列[An]的首相为A1= -1,前n项和为Sn,若 S10/S5=31/32,求limSn
问题描述:
等比数列[An]的首相为A1= -1,前n项和为Sn,若 S10/S5=31/32,求limSn
答
S10=a1(1-q^10)/(1-q) S5=a1(1-q^5)/(1-q) S10/S5=(1-q^10)/(1-q^5) =(1+q^5)(1-q^5)/(1-q^5) =1+q^5=31/32 q^5=-1/32 q=-1/2 所以lim Sn=a1/(1-q)=-1/(1+1/2)=-2/3