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alex.lupas@gmail.com
science forum beginner

Joined: 23 Feb 2006
Posts: 47

Posted: Sun Jul 16, 2006 3:48 am    Post subject: Sequence with factorials

For n in {2,3,...} let

L_n:= ((n+1)!)^{1/(n+1)}- (n!)^{1/n}=

=sqrt[n+1]{(n+1)!} -sqrt[n]{n!}, (LaTex) ,

W_n:= (n+1)/((n!)^{1/n}) = (n+1)/sqrt[n]{n!},

eps_n:= ((n+1)!)^{1/(n+1)}/((n!)^{1/n}) - 1 =

= sqrt[n+1]{(n+1)!}/sqrt[n]{n!} - 1 .

QUESTIONS [try without using Stirling's formula] :

A) lim_{n-->infty}L_n= ??

B) ((ln(W_n))*ln((1+eps_n)^{-1/eps_n}))/W_n = ??

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