Show that if p is a positive integer, then the power seriesk=0(pk)!(k!)p xkhas a radius

Chapter 9, Problem 59

(choose chapter or problem)

Show that if $p$ is a positive integer, then the power series

$\sum_{k=0}^{\infty} \frac{(p k) !}{(k !)^{p}} x^{k}$

has a radius of convergence of $1 / p^{p}$.

Equation Transcription:

$\sum\limits_{k=0}^{\infty{}}\frac{(pk)!}{(k!{)}^{p}}{x}^{k}$

$p$

$1/{{p}^{p}}^{\ }$

Text Transcription:

sum_k=0^ infinity (pk)!/ (k!)^p x^k

1/p^p.

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