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Grinstead-Snell-Probability
· Problem 3.1.9
Combinatorics
Mathematics · permutations
Problem
A more refined inequality for approximating
n
!
n!
n
!
is given by
2
π
n
(
n
e
)
n
e
1
/
(
12
n
+
1
)
<
n
!
<
2
π
n
(
n
e
)
n
e
1
/
(
12
n
)
.
\sqrt{2\pi n}\left(\frac{n}{e}\right)^n e^{1/(12n+1)} < n! < \sqrt{2\pi n}\left(\frac{n}{e}\right)^n e^{1/(12n)}.
2
π
n
(
e
n
)
n
e
1/
(
12
n
+
1
)
<
n
!
<
2
π
n
(
e
n
)
n
e
1/
(
12
n
)
.
Write a computer program to illustrate this inequality for
n
=
1
n = 1
n
=
1
to 9.
Related theory
permutations
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