Question

Lim an=A,证前n项几何平均的极限=A

Answer 1

设前n项几何平均=（a1a2...an）^(1/n)=m,则a1a2...an=m^n

前n项几何平均=（a1a2...anan+1）^(1/（n+1)=m,代入a1a2...an=m^n,an+1=A

得出m^n*A=m^（n+1）,即A=m,得证