已知数列an满足a1=3,An+1=2An+2^n (1)求证数列[An/2^n]是等差数列 (2)求an通项公式_数学解答

已知数列an满足a1=3,An+1=2An+2^n (1)求证数列[An/2^n]是等差数列 (2)求an通项公式

人气：268 ℃　时间：2019-12-12 14:24:38

解答

(1)证：a(n+1)=2an+2ⁿ等式两边同除以2^(n+1)a(n+1)/2^(n+1)=an/2ⁿ +1/2a(n+1)/2^(n+1)-an/2ⁿ=1/2,为定值.a1/2=3/2,数列{an/2ⁿ}是以3/2为首项,1/2为公差的等差数列.(2)an/2ⁿ=(3/2)+(n-...