Determine if the series converges or diverges.
∑
n
=
1
∞
(
1
5
−
8
n
5
)
n
\displaystyle {\sum_{{{n}={1}}}^{\infty}}{\left(\frac{{1}}{{5}}-\frac{{8}}{{n}^{{{5}}}}\right)}^{{n}}
n
=
1
∑
∞
(
5
1
−
n
5
8
)
n
Converges
Diverges
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