Test each of the following series for convergence by either the Comparison Test

Question

Test each of the following series for convergence by either the Comparison Test or the Limit Comparison Test. If either test can be applied to the series, enter CONV if it converges or DIV if it diverges. If neither test can be applied to the series, enter NA. (Note: this means that even if you know a given series converges by some other test, but the comparison tests cannot be applied to it, then you must enter NA rather than CONV.)

Test each of the following series for convergence by either the Comparison Test or the Limit Comparison Test. If either test can be applied to the series, enter CONV if it converges or DIV if it diverges. If neither test can be applied to the series, enter NA. (Note: this means that even if you know a given series converges by some other test, but the comparison tests cannot be applied to it, then you must enter NA rather than CONV.) 4n5/n8+3 4n5/n6+3 cos(n) n/4n+3 cos2(n) n/n5 (-1)n/7n

Explanation / Answer

1. Converges by regular comparison test (Compare to 5/n^3)

2. Diverges by regular comparison test (Compare to 3/n).

3. NA. Neither test works because not all terms are positive.

4. Converges by regular comparison test (Compare to 1/(n^4.5)

5. NA. Neither test works because it's alternating.

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