3^n
=(2+1)^n
=2^n+C(n,1)2^(n-1)+C(n,2)2^(n-2).
>2^n+n·2^(n-1)+C(n,2)2^(n-2)
=2^(n-1)·(2+n)+C(n,2)2^(n-2)
题目肯定有错
如n=3
3^3=27
(3-1)*2^3+1
=2×16
=32
27(3-1)*2^3+1=17，+1是没有括号的3^n=(2+1)^n=2^n+C(n,1)2^(n-1)+C(n,2)2^(n-2)+......+C(n,n-1)2^1+1>2^n+n[2^(n-1)+2^(n-2)+....+2^2+2^1]+1=2^n+n·2(1-2^(n-1) )/(1-2)+1=2^n+n·2(2^(n-1)-1)+1=2^n+n(2^n-2)+1=(n+1)2^n -2n+1=(n-1)2^n+2^(n+1)-2n+1因为2^(n+1)≥2n所以(n-1)2^n+2^(n+1)-2n+1>(n-1)2^n+1即3^n>(n-1)2^n+1