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1969 IMO Shortlist
64
Prove that (n!)!>n[(n-1)!]^{n!}
Prove that (n!)!>n[(n-1)!]^{n!}
Source:
October 4, 2010
Inequality
factorial
algebra
IMO Shortlist
IMO Longlist
Problem Statement
(
U
S
S
1
)
(USS 1)
(
U
SS
1
)
Prove that for a natural number
n
>
2
,
(
n
!
)
!
>
n
[
(
n
ā
1
)
!
]
n
!
.
n > 2, (n!)! > n[(n - 1)!]^{n!}.
n
>
2
,
(
n
!)!
>
n
[(
n
ā
1
)!
]
n
!
.
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