S3a) Use the Integral Test to determine the convergence or divergence of the following series. Remember to confirm the hypotheses of the Integral Test first. ∞ Σ n=1 n 1 + n² S3b) Determine the convergence or divergence of the following series by first writing it in the form 1+ ∞0 Σαη n=1 (Hint: You don't need to use the Integral Test with this one.) 1 1 1 1 + + + +. 2√2 3√/3 4√4 5√5

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…

00 n Does the series (-1)^n² Σ 1)^n² (²)" n=1 converge absolutely, converge conditionally, or diverge? Choose the correct answer below and, if necessary, fill in the answer box to complete your choice. O A. The series converges conditionally per the Alternating Series Test and because the limit used in the nth-Term Test is OB. The series converges absolutely since the corresponding series of absolute values is geometric with |r|= O C. The series diverges because the limit used in the nth-Term Test does not exist. D. The series converges absolutely because the limit used in the Ratio Test is O E. The series diverges because the limit used in the Ratio Test is not less than or equal to 1. OF. The series converges conditionally per Alternating Series Test and because the limit used in the Ratio Test is

a. Find the first four nonzero terms fo the Maclaurin series for the givenfunction.b. Write the power series using summation notationc. Determine the interval of convergence of the series. ?(?) = (5 + ?^2)^-1