设等比数列{an}的前n项和为Sn,若S10:S5=1:2,求S15:S5

2025-06-26 23:34:39
推荐回答(1个)
回答1:

S10=a1(1-q^10)/(1-q)
S5==a1(1-q^5)/(1-q)

所以(1-q^10)/(1-q^5)=1/2
1+q^5=1/2
q^5=-1/2

所以S15/S5
=(1-q^5)/(1-q^5)
=1+q^5+q^10
=1-1/2+1/4
=3/4