数列{an}满足a1=1,a(n+1)=2^(n+1)an/an+2^n(n∈N) (1)证明数列{2^n/an}是等差数列,
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![数列{an}满足a1=1,a(n+1)=2^(n+1)an/an+2^n(n∈N) (1)证明数列{2^n/an}是等差数列,](/uploads/image/z/2000106-18-6.jpg?t=%E6%95%B0%E5%88%97%7Ban%7D%E6%BB%A1%E8%B6%B3a1%3D1%2Ca%28n%2B1%29%3D2%5E%28n%2B1%29an%2Fan%2B2%5En%28n%E2%88%88N%29+%EF%BC%881%EF%BC%89%E8%AF%81%E6%98%8E%E6%95%B0%E5%88%97%7B2%5En%2Fan%7D%E6%98%AF%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2C)
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数列{an}满足a1=1,a(n+1)=2^(n+1)an/an+2^n(n∈N) (1)证明数列{2^n/an}是等差数列,
数列{an}满足a1=1,a(n+1)=2^(n+1)an/an+2^n(n∈N) (1)证明数列{2^n/an}是等差数列,
数列{an}满足a1=1,a(n+1)=2^(n+1)an/an+2^n(n∈N) (1)证明数列{2^n/an}是等差数列,
同除以2^(n+1)
得a(n+1)/2^(n+1)=an/(an+2^n)
倒过来得2^(n+1)/a(n+1)=1+[(2^n)/an]
[2^(n+1)/a(n+1)]-[(2^n)/an]=1
得证
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