a(n+1)/an=2^n
于是
an/a(n-1)=2^(n-1)
a(n-1)/a(n-2)=2^(n-2)
...
a2/a1=2^1
相乘有
an/a1=2^(n-1)*2^(n-2)*...*2^1=2^((n-1)+(n-2)+...+1)=2^(n(n-1)/2)
于是an=a1*2^(n(n-1)/2)=2^(n(n-1)/2)
若数列an满足a1=1,an+1=2^nan...
1个回答
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