Use the Limit Comparison Test to determine if the series converges.
∑
k
=
1
∞
k
+
8
k
(
k
−
5
)
(
k
+
1
)
\displaystyle {\sum_{{{k}={1}}}^{\infty}}\ \frac{{{k}+{8}}}{{{k}{\left({k}-{5}\right)}{\left({k}+{1}\right)}}}
k
=
1
∑
∞
k
(
k
−
5
)
(
k
+
1
)
k
+
8
Diverges
Converges
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