alex.lupas@gmail.com
science forum beginner
Joined: 23 Feb 2006
Posts: 47
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 Posted: Sun Jul 16, 2006 3:48 am Post subject:
Sequence with factorials
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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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