For each of the following series, tell whether or not you can apply the 3-condit

Question

For each of the following series, tell whether or not you can apply the 3-condition test (i.e. the alternating series test). Enter D if the series diverges by this test, C if the series converges by this test, and N if you cannot apply this test (even if you know how the series behaves by some other test). Sigma_n = 2^infinity (-1)^n (n^4 + 2n)/n^3 Sigma_n = 1^infinity (-1)^n cos(n)/n^2 Sigma_n = 1^infinity (-1)^n (n^3 + 1)/n^4 + 1 Sigma_n = 1^infinity (-1)^n/n^5 Sigma_n = 1^infinity (-1)^n (n^3 + 1)/n^3 + 7 Sigma_n = 1^infinity (-1)^n (n^10 + 1)/e^n

Explanation / Answer

1. Ratio and root tests are inconclusive. Answer: N

2. By the comparison test, it converges. Answer: C

3. By the alternating series test, it converges. Answer: C

4. By the alternating series test, it converges. Answer: C

5. Ratio and root tests are inconclusive. Answer: N

6. By the alternating series test, it converges. Answer: C

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