令Bn=AnAn+1,则数列{Bn}是公比为q（q大于0）的等比数列An+1An+2=Bn+1=Bn*qAn+2An+3=Bn+2=Bn*q²Bn+Bn+1＞Bn+2Bn+Bn*q＞Bn*q²因为Bn＞0所以1+q＞q²且q＞0所以0＜q＜(1+√5)/2
0＜q＜(1+√5)/2
