lim-n-x-n-n-1-

Question Number 132367 by Raxreedoroid last updated on 13/Feb/21

\lim_{n \to \infty} \frac{x^{n}}{Γ (n + 1)}

Answered by TheSupreme last updated on 13/Feb/21

i f n \in N \to Γ (n + 1) = n!

\lim \frac{x^{n}}{n!} = 0 \forall x \in R_{0}^{+}

\sup (\frac{x^{n}}{n!}) = \infty w i t h x \in R_{0}^{+}

s e t A = [0, a] \in R_{0}^{+}

s u p (\frac{x^{n}}{n!}) = \frac{a^{n}}{n!}

{l i m}_{n} s u p (f_{n} (x)) = 0 \forall x \in A, \forall a \in R^{+}

c o n v e r g e n z a p u n t u a l e i n R_{0}^{+}

c o n v e r g e n z a a s s o l u t a \forall x \in A, \forall a \in R^{+}