Please show how this diverges with the nth term divergence test please. Exactly

Question

Please show how this diverges with the nth term divergence test please.

Exactly one of the following is true about the series Sigma(-1)n 2n2 /3 + 5n2. Mark only that one. It converges absolutely by the ratio test. It converges by the ratio test. It diverges by the ratio test. It converges absolutely because a p-series with p > 1 converges. It converges conditionally. It converges because it is absolutely convergent and an absolutely convergent series is also convergent. It converges by the Alternating Series test. It diverges by the Alternating Series test. It diverges because it's a p-series with p > l. It diverges by the nth term divergence test.

Explanation / Answer

Take the lim as n approaches

Use l'hospital's rule and you get the lim n-> = 4/10 since the limit does NOT = 0 then it diverges

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