In this homework, you will determine if the following series converges or diverges. n-1 n=1 +n + 14 a) Look at the sequence terms. As n , the sequence of terms n-1 n3+n+14 behaves like for some power p. What is the value of p? Show all work or write out a full explanation 1 np for your chosen power of p. b) For your chosen power of p, does the series and indicate which test you used. 1 converge or diverge? Justify your answer, n=1 c) Make a prediction. Based on the status of 1 do we expect 1 to n=. converge or diverge. n= n + n + 14 d) Now justify your prediction with either the (Series) Comparison Test or the Limit Com- parison Test. Be sure to indicate which test you are going to preform and tell us why you use this test. A sentence should suffice. Justify all steps in your test (i.e. if comparison, justify the inequality; if limit comparison, show all steps in the computation of the limit). Your submission will be graded on the quality of the solution. The grader should be able to understand what you are doing and why you are doing it; sentences such as: "In order to apply table entry 25, we need to complete the square in the denominator" help accomplish that. You are required to use words, phrases, and sentences, and failure to do so will result in little to no credit on the assignment. In addition, appropriate notation should be used, and used correctly.