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MATH 101 Quiz #6 (v.A1) Last Name: Friday, April 1 First Name: Grade: Student-No: Section: Very short answer question P 1. 1 mark Suppose you wanted to use the Limit Comparison Test on the series ∞ n=0 an where n an an = 23n+n . Write down a sequence {b } such that lim exists and is nonzero. (You don’t n n→∞ bn +1 have to carry out the Limit Comparison Test; just write the formula for the bn .) Answer: Short answer questions—you must show your work P 2 (−1)n−1 2. 2 marks It is known that ∞ = π12 (you don’t have to show this). Find N so that n=1 n2 2 SN , the N th partial sum of the series, satisfies | π12 − SN | ≤ 10−6 . Be sure to say why your method can be applied to this particular series. Answer: 3. 2 marks Does the series ∞ √ X n cos n n=5 Explain your answer. n2 − 1 converge conditionally, converge absolutely, or diverge? Long answer question—you must show your work 4. 5 marks Find the radius of convergence and interval of convergence of the series n ∞ X (−1)n x + 2 . n + 1 2 n=0