已知数列{AN}满足A1=1,AN+1=2AN+2的N次方.
题目
已知数列{AN}满足A1=1,AN+1=2AN+2的N次方.
[1]设BN=AN/2的N次方,求证：数列{BN}是等差数列；[2]求数列{AN}的通项公式
答案
1.a_(1)=1,a_(n+1)=2a_(n)+2^(n)----------------1b_(n)=a_(n)/2^(n)将式子1左右两边同时除以 2^(n+1),则:b_(n+1)=b_(n)+1/2b_(1)=a_(1)/2^(1)=1/2所以数列{bn}是首项为1/2,公差为1/2的等差数列.2.b_(n)=n/2.a_(n)=b...
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