设数列an满足 a1=5/6,且an=1/3a（n-1）+1/3 求证数列an-1/2为等比数列并求an的通项公式与前n项和Sn_数学解答

设数列an满足 a1=5/6,且an=1/3a（n-1）+1/3 求证数列an-1/2为等比数列
并求an的通项公式与前n项和Sn

人气：370 ℃　时间：2020-01-30 14:55:15

解答

an=(1/3)a(n-1)+1/3an -1/2 = (1/3)[a(n-1) -1/2](an -1/2)/[a(n-1) -1/2] =1/3=>{an-1/2}为等比数列(an -1/2)/[a(n-1) -1/2] =1/3(an -1/2)/[a1 -1/2] =(1/3)^(n-1)an-1/2 = (1/3)^n an = 1/2 + (1/3)^nSn =a1+a2+....