等比数列an的各项都是正数,a2,1/2a3,a1成等差数列,则(a4+a5)/(a5+a6)的值为多

问题描述:

等比数列an的各项都是正数,a2,1/2a3,a1成等差数列,则(a4+a5)/(a5+a6)的值为多

因为a2,1/2a3,a1成等差数列
故2×1/2a3=a2+a1
将a2=a1q,a3=a1q^2代入上式得
q^2=q+1
q^2-q-1=0
又q>0
故q=(√5+1)/2
(a4+a5)/(a5+a6)=1/q=(√5-1)/2