At least one of the answers above is NOT correct. Consider the series infinity s

Question

At least one of the answers above is NOT correct. Consider the series infinity sigma n = 1 (-1)^n n/n^2 + 4 Attempt the Ratio Test to determine whether the series converges. |an + 1/an| = L = lim n righatarrow infinity |an + 1/an| = Enter the numerical value of the limit L if it converges, INF if it diverges to infinity, or DIV if it diverges but not to infinity. Which of the following statements is true? The Ratio Test says that the series converges absolutely. The Ratio Test says that the series diverges. The Ratio Test says that the series converges conditionally.

Explanation / Answer

an = n/(n2 +4)

an+1 = (n +1)/[(n +1)2 +4] = (n +1)/(n2 +2n +5)

|an+1/an| = |[(n +1)/(n2 +2n +5)] / [n/(n2 +4)] |

= |(n +1)(n2 +4) / [n(n2 +2n +5)]|

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