Super Hard Limit

[Papabile]

Hi, I have problem with that limes. Can you help me?
a_n=(1^n+2^n+3^n+...+n^n)/(n^n) , n>1

I)Prove that the sequence (a_n) is increasing.
II)Compute lim(n→∞) a_n.

 

[tkhunny]

Hi, I have problem with that limes. Can you help me?
a_n=(1^n+2^n+3^n+...+n^n)/(n^n) , n>1

I)Prove that the sequence (a_n) is increasing.
II)Compute lim(n→∞) a_n.

Perhaps rewrite a_n = (1/n)^n + (2/n)^n + (3/n)^n + ... + ((n-1)/n)^n + 1