设等比数列{an]的公比为q,前n项和为Sn,且S10=8,则(S20)/(1+q^10)=

问题描述:

设等比数列{an]的公比为q,前n项和为Sn,且S10=8,则(S20)/(1+q^10)=

S10=a1(1-q^n)/(1-q)=a1(1-q^10)/(1-q)=8
S20/(1+q^10)=a1(1-q^20)/(1-q)/(1+q^10)=a1(1+q^10)(1-q^10)/(1-q)/(1+q^10)=a1(1-q^10)/(1-q)=8