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MATH 101 Quiz #6 (v.A2) 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 +2 an = 53n +n . Write down a sequence {bn } such that limn→∞ abnn exists and is nonzero. (You don’t 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 | ≤ 35−2 . Be sure to say why your method can be applied to this particular series. Answer: 3. 2 marks Does the series ∞ X n sin n n=5 Explain your answer. n3 − 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 + 3 . n + 1 3 n=0