等比数列中前n项和为Sn 若S6/S2=7则S8/S4为?
问题描述：
等比数列中前n项和为Sn 若S6/S2=7则S8/S4为?
答
S6/S2=7[a1(1-q^6)/(1-q)]/[a1(1-q^2)/(1-q)]=7(1-q^6)/(1-q^2)=7(1-q^2)(1+q^2+q^4)/(1-q^2)=71+q^2+q^4=7q^4+q^2-6=0(q^2+3)(q^2-2)=0因为q^2+3>0所以q^2-2=0q^2=2S8/S4=[a1(1-q^8)/(1-q)]/[a1(1-q^4)/(1-q)]=(1-q...