※ 引述《jimlucky (......)》之銘言：
: lim (n!)^(1/n)
: n->00 -----------
: n
Methods:
(1) Try to use the famous formula:
lim inf b_n ≦ lim inf (a_n)^(1/n) ≦ lim sup (a_n)^(1/n) ≦ lim sup b_n,
where b_n := (a_(n+1))/a_n.
So, you need to find some suitable "a_n".
(2) Consider the improper Riemann integral: First, you need to take log to
the sequence {n!/(n^n)}^(1/n). Leave to you.
(3) Think about "e", and (1 + 1/n)^n ＜ e ＜ (1 + 1/n)^(n+1).
(4) Use the famous Stirling formula.
(5) etc.
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 122.116.231.200
※ 編輯: math1209 來自: 122.116.231.200 (12/16 04:54)