Identify / Claim whether the series converges or diverges and apply an appropriate test to prove your claim. (Divergence test, geometric series test, telescoping series, integral test, p-series test, limit comparison test, ratio test, root test, or alternating series test)

$\sum_{k=1}^{\infty} \frac{\sqrt{4 k^{3}+k^{5}}}{k^{2}+5 k^{3}}$

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Identify / Claim whether the series converges or diverges and apply an appropriate test to prove your claim. (Divergence test, geometric series test, telescoping series, integral test, p-series test, limit comparison test, ratio test, root test, or alternating series test)

$\sum_{k=1}^{\infty} \frac{\sqrt{4 k^{3}+k^{5}}}{k^{2}+5 k^{3}}$

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