A community for students.
Here's the question you clicked on:
← 55 members online
 0 viewing
watchmath
 5 years ago
Compute the limit
\[ \lim_{n\to\infty}\frac{n!}{n^n}\]
watchmath
 5 years ago
Compute the limit \[ \lim_{n\to\infty}\frac{n!}{n^n}\]

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0let y=n!/n^n lny=\[\sum_{r=0}^{n}\ln(nr)/n\] now ln((nr)/n)=ln(1r/n) as n>infinity so r/n=0 so ln(1r/n)=ln(1)=0; lny=0 y=1 so the limit is 1

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.0Something wrong with your argument dipankar. I found the answer \[0<\frac{n!}{n^n}<\frac{1\cdot n^{n1}}{n^n}=\frac{1}{n}\] By squeeze theorem, then the limit is zero.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.