若数列an满足a1=1,an+1=2^nan...

问题描述:

若数列an满足a1=1,an+1=2^nan...
若数列an满足a1=1,a(n+1)=2^n·an,则数列an的通项公式?

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)