For each series below identify which test could be used to determine convergence or divergence. More than one test may apply to a particular series but you must use each of the tests below at least once. a) nt-term test b) p-series test c) 1. N 2. 3. 4. Geometric series test M8 M8 M8 M8 77=1 n 2n n=13n-2 n n=1(n² + 1)² d) Telescoping series test e) Integral test f) Direct comparison test g) Limit comparison test h) Alternating series test i) Ratio test Answers: 1. 2. 3. 4.

Given below are 7 series. Pick the most appropriate test to determine if the given series converges, converges absolutely, or diverges.

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…

Determine whether each series converges or diverges. Circle your choice and state which convergence test you used. Give reason for your choices. (a) n3/2 diverges Test: converges n=1 Reason: (b) (-1)n 2n Test: diverges converges n=0 Reason: (e) * (1+)" Test: diverges converges n=1 Reason: