数列{an}中,a1=2,a2=3,且{anan+1}是以3为公比数列,记bn=a2n-1+a2n,求证：{bn}是等比数列
问题描述：
数列{an}中,a1=2,a2=3,且{anan+1}是以3为公比数列,记bn=a2n-1+a2n,求证：{bn}是等比数列
答
(an*an+1)/(an-1*an)=3
=> an+1/an-1=3
=> a2n=3^n,a2n-1=2*3^(n-1)
=> bn=5*3^(n-1)