The Direct Comparison Test Suppose that we have decided to investigate the convergence or divergence of the series using the Direct Comparison Test. Select all of the statements below that are true. OA. The given series diverges since for n >1 and is a divergent p-series (p = ). n=1 B. The given series converges since < for n 21 and E is a convergent p-series (p = 2). n=1 OC. The given series diverges since < for n >1 and E is the divergent Harmonic series. OD. The given series diverges since for n >1 and diverges by the integral test. =1 2n Note: there may be more than one correct answer. Select all that apply.

The issue of convergence or divergence of some series can be answered by several different approaches (series tests), and each would give the answer independently. k2 Consider the series E- Answer the questions below regarding some of the tests one might try in order to determine whether the series converges or diverges. k = 1 (e) Would the ratio test be conclusive here? Select the correct choice below and, it necessary, till in the answer box within your choice. O A. Applying the ratio test gives r= 1. Therefore, the ratio test is inconclusive. O B. Applying the ratio test gives r= (type an exact value, or o or – o0). Since r 1, the series DIVERGES by the ratio test. (f) Can the alternating series test be applied here? Select the correct choice below and, if necessary, fill in the answer box within your choice. For this one, we let a, be the m O A. This is an alternating series and hence the alternating series test can be applied. It is clear that the terms a, are decreasing and that…

EXCERCISE 3 • Indicate whether the given series converges or diverges, if it is converges find its sum. -k-2 b. k=1 1 4 d. Σ3 k=1 1 k+1 7