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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

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anonymous
 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

anonymous
 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

anonymous
 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

anonymous
 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

anonymous
 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

anonymous
 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?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you "become their fan"

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

anonymous
 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

anonymous
 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
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