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Find out whether the series given below converges or diverges. Σ∞ n=3 1/n√n^2 - 5 Choose the correct answer below. A. The comparison test with Σ 1/n shows that the series diverges. B. The comparison test with Σ 1/n^3/2 shows that the series diverges. C. The comparison test with Σ 1/n shows that the series converges. D. The comparison test with Σ 1/n^3/2 shows that the series converges.

Find out whether the series given below converges or diverges. Σ∞ n=3 1/n√n^2 - 5 Choose the correct answer below. A. The comparison test with Σ 1/n shows that the series diverges. B. The comparison test with Σ 1/n^3/2 shows that the series diverges. C. The comparison test with Σ 1/n shows that the series converges. D. The comparison test with Σ 1/n^3/2 shows that the series converges.

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Find out whether the series given below converges or diverges. Σ∞ n=3 1/n√n^2 - 5 Choose the correct answer below. A. The comparison test with Σ 1/n shows that the series diverges. B. The comparison test with Σ 1/n^3/2 shows that the series diverges. C. The comparison test with Σ 1/n shows that the series converges. D. The comparison test with Σ 1/n^3/2 shows that the series converges.

Explanation & Steps

In the given question:

                                                                                                  a_n = \frac{1}{n\sqrt{n^2 -5}}

Step 1) Determine the suitable bn so that direct comparison test can be applied between an and bn. Before applying comparison test, conditions for an and bn need to be checked.

Step 2) Next apply p-series test to determine convergence of \sum b_n.

Step 3) Based on convergence of \sum b_n, decide the convergence of \sum a_n.

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