lim[(n+2)log2(n+2)-2(n+1)log2(n+1)+nlog2n]是0还是1,书上答案是1,觉得有点怪n→∞

Question

lim[(n+2)log2(n+2)-2(n+1)log2(n+1)+nlog2n]是0还是1,书上答案是1,觉得有点怪 n→∞

Answer 1

原式=lim(n->∞){log2[(n+2)^(n+2)]-log2[(n+1)^(2n+2)]+log2(n^n)}
=lim(n->∞)log2{[(n+2)^(n+2)](n^n)/[(n+1)^(2n+2)]}
=lim(n->∞)log2{[(1+2/n)^(n+2)]/[(1+1/n)^(2n+2)]}
=log2(1)
=0
显然答案是错的!