在数列an中,a1=2,a2=3且{an*a(n+1)}(n∈N*)是以3为公比的等比数列数列{an}中,a1=2,a2=3,且{anan+1}是以3为公比的等比数列,若bn=2a2n-1+a2n(n为正整数)1)分别求a3,a4,a5,a62)求证{bn}是等比数列修改:bn=a2n-
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![在数列an中,a1=2,a2=3且{an*a(n+1)}(n∈N*)是以3为公比的等比数列数列{an}中,a1=2,a2=3,且{anan+1}是以3为公比的等比数列,若bn=2a2n-1+a2n(n为正整数)1)分别求a3,a4,a5,a62)求证{bn}是等比数列修改:bn=a2n-](/uploads/image/z/13940748-36-8.jpg?t=%E5%9C%A8%E6%95%B0%E5%88%97an%E4%B8%AD%2Ca1%3D2%2Ca2%3D3%E4%B8%94%7Ban%2Aa%28n%2B1%29%7D%28n%E2%88%88N%2A%29%E6%98%AF%E4%BB%A53%E4%B8%BA%E5%85%AC%E6%AF%94%E7%9A%84%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%E6%95%B0%E5%88%97%EF%BD%9Ban%EF%BD%9D%E4%B8%AD%2Ca1%EF%BC%9D2%2Ca2%3D3%2C%E4%B8%94%EF%BD%9Banan%2B1%EF%BD%9D%E6%98%AF%E4%BB%A53%E4%B8%BA%E5%85%AC%E6%AF%94%E7%9A%84%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%E8%8B%A5bn%3D2a2n-1%2Ba2n%28n%E4%B8%BA%E6%AD%A3%E6%95%B4%E6%95%B0%291%29%E5%88%86%E5%88%AB%E6%B1%82a3%2Ca4%2Ca5%2Ca62%29%E6%B1%82%E8%AF%81%7Bbn%7D%E6%98%AF%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%E4%BF%AE%E6%94%B9%EF%BC%9Abn%3Da2n-)
在数列an中,a1=2,a2=3且{an*a(n+1)}(n∈N*)是以3为公比的等比数列数列{an}中,a1=2,a2=3,且{anan+1}是以3为公比的等比数列,若bn=2a2n-1+a2n(n为正整数)1)分别求a3,a4,a5,a62)求证{bn}是等比数列修改:bn=a2n-
在数列an中,a1=2,a2=3且{an*a(n+1)}(n∈N*)是以3为公比的等比数列
数列{an}中,a1=2,a2=3,且{anan+1}是以3为公比的等比数列,若bn=2a2n-1+a2n(n为正整数)
1)分别求a3,a4,a5,a6
2)求证{bn}是等比数列
修改:bn=a2n-1+a2n(n为正整数)
在数列an中,a1=2,a2=3且{an*a(n+1)}(n∈N*)是以3为公比的等比数列数列{an}中,a1=2,a2=3,且{anan+1}是以3为公比的等比数列,若bn=2a2n-1+a2n(n为正整数)1)分别求a3,a4,a5,a62)求证{bn}是等比数列修改:bn=a2n-
a1a2=6
a2a3=3a1a2=18,a3=18/a2=6
a3a4=3a2a3=54,a4=9
同样可得:a5=18,a6=27
A2n-1A2n-2=3*(A2n-3A2n-2),
A2n-3=A2n-1/3
同样可得:
A2n-2=A2n/3
A2n+1=3A2n-1
A2n+2=3A2n
Bn-1*Bn+1=(2A2(n-1)-1+A2(n-1))*(2A2(n+1)-1+A2(n+1))
=(2A2n-3+A2n-2)*(2A2n+1+A2n+2)
=(1/3)*(2A2n-1+A2n)*(3)*(2A2n-1+A2n)
=(2A2n-1+A2n)^2
=Bn^2
所以Bn成等比数列
按你修改的也是同样的证明,从证明过程中可以发现,与前面有没有2无关!
Bn-1*Bn+1=(A2(n-1)-1+A2(n-1))*(A2(n+1)-1+A2(n+1))
=(A2n-3+A2n-2)*(A2n+1+A2n+2)
=(1/3)*(A2n-1+A2n)*(3)*(A2n-1+A2n)
=(A2n-1+A2n)^2
=Bn^2