Answer
Converges
Work Step by Step
a) Factoring out the constant $ \frac{4k^2-2k+6}{8k^7+k-8}$ leaves
$$\Sigma^m_{k=1} \frac{4k^2-2k+6}{8k^7+k-8}$$
This is a p-series with p>1, so the series Converges.
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