已知数列an满足:a1=m,a(n+1)=2an+3^(n-1),(1)设bn=a(n+1)/3^n,求数列bn(2)若对任意正整数n,都有a(n+1)≥an,求m的最小值
问题描述:
已知数列an满足:a1=m,a(n+1)=2an+3^(n-1),(1)设bn=a(n+1)/3^n,求数列bn(2)若对任意正整数n,都有a(n+1)≥an,求m的最小值
答
(1)a(n+1)=2an+3^(n-1)=2an+[3^n-2*3^(n-1)]则a(n+1)-3^n=2[an-3^(n-1)]{a(n+1)-3^n}是公比q=2的等比数列a2=2a1+1=2m+1a(n+1)-3^n=(a2-3)*q^(n-1)=(m-1)*2^na(n+1)=(m-1)*2^n+3^nbn=a(n+1)/3^n=(m-1)*(2/3)^...