等比数列{an}中,an大于0,n属于正整数,求证{lgan}是等差数列,{根号下an}是等比数列

来源：学生作业帮编辑：拍题作业网作业帮分类：数学作业时间：2024/04/28 00:41:36

解析：∵{an}是等比数列,令首项=a1,公比=q∴an=a1*q^(n-1),an＞0,n∈N+
∵log[an]-log[a(n-1)]
=log[a1*q^(n-1)]-log[a1*q^(n-2)]
=log{[a1*q^(n-1)]/[a1*q^(n-2)]}
=logq=定值
∴{logan}是首项loga1,公差=logq的等差数列
∵√an/√a(n-1)=√an/a(n-1)=√q=定值
∴{√an}是首项=√a1,公比=√q的等比数列

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