Given the series
p
n
=
∑
n
=
1
∞
(
4
n
+
4
)
!
4
n
n
!
\displaystyle \ \ {p}_{{n}}={\sum_{{{n}={1}}}^{\infty}}\frac{{{\left({4}{n}+{4}\right)}!}}{{{4}^{{n}}{n}!}}
p
n
=
n
=
1
∑
∞
4
n
n
!
(
4
n
+
4
)
!
Find
lim
n
→
∞
∣
p
n
+
1
p
n
∣
=
\displaystyle \ \ \lim_{{{n}\to\infty}}{\left|{\frac{{{p}_{{{n}+{1}}}}}{{{p}_{{n}}}}}\right|}=
n
→
∞
lim
∣
∣
p
n
p
n
+
1
∣
∣
=
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Enter DNE for Does Not Exist, oo for Infinity