n→∞ lim(1^n+2^n+...+100^n)^(1/n)

(1^n+2^n+...+100^n)^(1/n) =100[(1/100)^n+(2/100)^n+...+1^n)]^(1/n) 而 1=<[(1/100)^n+(2/100)^n+...+1^n)]^(1/n) <(1+1+...+1)^(1/n)=n^(1/n)→1 (n→∞ ) 所以n→∞ lim[(1/100)^n+(2/100)^n+...+1^n)]^(1/