A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
does this sequence converge or diverge?
(n!)/(n^n) and the reason
anonymous
 5 years ago
does this sequence converge or diverge? (n!)/(n^n) and the reason

This Question is Closed

sandra
 5 years ago
Best ResponseYou've already chosen the best response.0this converges to zero since eventually n! expands into n*....n(n1) [i.e. 1], while the last multiple of n^n is still n. i.e. once n is big enough the last divisor is obviously bigger enough to bring the number to zero

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hey sandra you dont have a better reason?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i dont buy this argument

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how about consider x! / x^x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what you wrote isnt obvious , sorry

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0we can make x! continuous using gamma function

sandra
 5 years ago
Best ResponseYou've already chosen the best response.0hmmm, not sure about that =) can you explain?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0well you didnt show it converges

sandra
 5 years ago
Best ResponseYou've already chosen the best response.0yeah I know, I gave the best reasoning I could heh

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Did you guys try the ratio test?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ratio test is for series, this is a sequence

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0or maybe im wrong, i havent see ratio test for sequences

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how about a sandwich theorem

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0n*n >= n * n1 n*n*n > = n * n1 n  2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so by induction we have

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0n * n1 * n2 / n*n*n < = 1

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it is strictly less than 1

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0n* n > (n1)(n2) for n >= 1

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok so divide out the first n

sandra
 5 years ago
Best ResponseYou've already chosen the best response.0ok, spolier alert... this is a bit beyond my current understanding, but I think the by induction track sounded good... http://www.physicsforums.com/showthread.php?t=195508

sandra
 5 years ago
Best ResponseYou've already chosen the best response.0the root solution is way over my head

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sandra i made you a hero

sandra
 5 years ago
Best ResponseYou've already chosen the best response.0I'm already your fan, so not much I can do :p

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0How do you give points to people?

sandra
 5 years ago
Best ResponseYou've already chosen the best response.0I think they should add per answer type ratings

sandra
 5 years ago
Best ResponseYou've already chosen the best response.0something like "best answer", or "thanks" or something. one more thing to collect :p

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I can't find "become their fan"

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0this is a tough question

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0see , the series 1/n diverges, but the sequence 1/n converges to zero when you take the limit

sandra
 5 years ago
Best ResponseYou've already chosen the best response.0hmmm jkwon, should be right by the person's name , e.g. right above my reply HERE

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0we know n! > n1 * n2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i think we can use the fact that its less than 1 and decreasing
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.