数列an满足a1=2,an+1(n+1为下标)-=2n+1n+1为上标)*an/(n+1/2)an+2的n次方

题目

数列an满足a1=2,an+1(n+1为下标)-=2n+1n+1为上标)*an/(n+1/2)an+2的n次方
（1）设bn=2的n次方除以an,求数列{bn}的通项公式
（2）设cn=1/n（n+1）an+1（n+1为下标）

答案

你问的是不是这样?a(n+1)=2^(n+1)an/[(n+1/2)an+2^n](1)易得2^(n+1)/a(n+1)=[(n+1/2)an+2^n]/an=n+1/2+2^n/an即b(n+1)=bn+n+1/2bn=b(n-1)+(n-1)+1/2=b1+1+2+……+(n-1)+1/2(n-1)=1+1/2[n(n-1)]+1/2(n-1)=1/2(n^2+1)(...