已知数列{An}满足A1=1,An+1=2An+2^n.求证数列An/2是等差数列_数学解答

已知数列{An}满足A1=1,An+1=2An+2^n.求证数列An/2是等差数列

人气：398 ℃　时间：2020-09-29 21:30:35

解答

你应该是抄错题了吧- -
A(n+1)=2An+2^n等式两边同时除以2^(n+1)
有A(n+1)/2^n+1=An/2^n+1/2
设Bn=An/2^n
则B(n+1)=Bn+0.5
Bn是等差数列
即An/2^n是等差数列