P Papabile New member Joined Dec 6, 2018 Messages 3 Jan 24, 2019 #1 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.
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 Moderator Staff member Joined Apr 12, 2005 Messages 11,325 Jan 24, 2019 #2 Papabile said: 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. Click to expand... Perhaps rewrite a_n = (1/n)^n + (2/n)^n + (3/n)^n + ... + ((n-1)/n)^n + 1
Papabile said: 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. Click to expand... Perhaps rewrite a_n = (1/n)^n + (2/n)^n + (3/n)^n + ... + ((n-1)/n)^n + 1
