Math 280 Take Home Quiz #6 Name___________________________ 20 points (OPTIONAL SPRING BREAK QUIZ) YOUR WORK MUST BE YOUR OWN Vanden Eynden, Spring 21 While I may have referred to the text or notes or used my calculator, all the work shown on this quiz is my own, without help from anyone else or apps/sites like Chegg or WolframAlpha.com. Signature____________________ (a) For each series below, determine whether the series CONVERGES or DIVERGES. Show all work and clearly explain your reasoning for each answer naming any relevant theorems, tests, or facts about the series you used to reach your conclusion. (b) IF POSSIBLE, find the exact sum of the series (no decimal approximations!) 16 64 256 1024 − + − + . . . 5 25 125 625 1. 5− 4 + 2. 9 − 2n 2  2 n =1 3n + 7n + 2    3.  3 n   2 n+1 n =1 5n n =1 4.  Math 280 Take Home Quiz #6 Name___________________________ 20 points (OPTIONAL SPRING BREAK QUIZ) YOUR WORK MUST BE YOUR OWN Vanden Eynden, Spring 21 5. Use the integral test to determine if the following series converges or diverges. First, show that the series satisfies the three conditions of the Integral Test. This must include an analysis of the derivative to prove that the terms are decreasing from some N on.  n2  n3 + 4 n =1
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