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Lebl-Basic-Analysis-I
· Problem 2.2.16
Sequences and Series
Mathematics · facts-about-limits-of-sequences
Problem
Prove that
{
(
n
!
)
1
/
n
}
n
=
1
∞
\{(n!)^{1/n}\}_{n=1}^\infty
{(
n
!
)
1/
n
}
n
=
1
∞
is unbounded. Hint: Show that for every
C
>
0
C > 0
C
>
0
,
{
C
n
n
!
}
n
=
1
∞
\left\{\dfrac{C^n}{n!}\right\}_{n=1}^\infty
{
n
!
C
n
}
n
=
1
∞
converges to zero.
Related theory
Sequences Convergence Cauchy Sequences Subsequences
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