答案：lim[(1^n + 2^n + 3^n + 4^n)]^(1/n)=lim[ 4^n * ((1/4)^n + (2/4)^n + (3/4)^n + 1)]^(1/n) = lim [4^n]^(1/n)*lim [(1/4)^n + (2/4)^n + (3/4)^n + 1)]^(1/n) = 4 * lim [(1/4)^n + (2/4)^n + (3/4)^n + 1)]...