在数列{an}中,已知a1=4/3,a2=13/9,当n≥2,且n∈N*时,有a(n+1)=4/3an-1/3a(n-1)(1)若bn=a(n+1)-an(n∈N*),求证数列{bn}是等比数列(2)求证:对任意n∈N*,都有4/3≤an<3/2
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![在数列{an}中,已知a1=4/3,a2=13/9,当n≥2,且n∈N*时,有a(n+1)=4/3an-1/3a(n-1)(1)若bn=a(n+1)-an(n∈N*),求证数列{bn}是等比数列(2)求证:对任意n∈N*,都有4/3≤an<3/2](/uploads/image/z/7230908-20-8.jpg?t=%E5%9C%A8%E6%95%B0%E5%88%97%7Ban%7D%E4%B8%AD%2C%E5%B7%B2%E7%9F%A5a1%3D4%2F3%2Ca2%3D13%2F9%2C%E5%BD%93n%E2%89%A52%2C%E4%B8%94n%E2%88%88N%2A%E6%97%B6%2C%E6%9C%89a%EF%BC%88n%2B1%29%3D4%2F3an-1%2F3a%28n-1%29%EF%BC%881%EF%BC%89%E8%8B%A5bn%3Da%EF%BC%88n%2B1%29-an%EF%BC%88n%E2%88%88N%2A%EF%BC%89%2C%E6%B1%82%E8%AF%81%E6%95%B0%E5%88%97%7Bbn%7D%E6%98%AF%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%EF%BC%882%EF%BC%89%E6%B1%82%E8%AF%81%EF%BC%9A%E5%AF%B9%E4%BB%BB%E6%84%8Fn%E2%88%88N%2A%2C%E9%83%BD%E6%9C%894%2F3%E2%89%A4an%EF%BC%9C3%2F2)
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