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
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
并求an的通项公式与前n项和Sn
数学人气:353 ℃时间:2020-01-30 14:55:15
优质解答
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+....
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