Section 10.6 Alternating Series Test

Make sure you read the questions very carefully and see on what its being asked for. Please be very careful with this assignment.

MATH 1522: SECTION 10.6 WRITTEN ASSIGNMENT For this class, there is only one way that we can check that a series converges conditionally, which we cover in this assignment. Consider the series E (-1)" n In(n) n=2 for the rest of the assignment. 1. Apply the alternating series test to show that the series converges. Show all the compu- tations needed to apply the test. 2. Take the absolute values of the terms of the series to obtain a new series of all positive terms. Show that the resulting series diverges. State the convergence test you're using and show all the necessary computations needed to apply the test. This assignment shows that the original series (-1)" n In(n) n=2 converges conditionally. Part #1 shows that it converges, while part #2 shows that it does not converge absolutely. This is the process necessary to show a series converges condition- ally. It's worth keeping this process in mind, since it may not be separated into parts like this in the future