Math 155 Exam 3-Sample 2006

Math 155 Exam 3-Sample 2006 - Math 155 Section 02 Calculus...

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Math 155 Section 02 Calculus II Exam 3—Sample 1. If { a n }is given, list the first 5 terms. If the first 5 first are given, find a formula for { a n }. For all, a) find the lim n →∞ a n , b) tell whether the sequence/series converges or diverges based on lim n →∞ a n . Write conv. for convergent, div. for divergent, and N/A if not applicable. { a n } n =1 First five terms lim n →∞ a n Sequence { a n } conv. or div.? Series Σ a n conv. or div.? { } 0, ln 1 / 2 , ln 1 / 3 , ln 1 / 4 , ln 1 / 5 ,... { } 1, e –1 , e –4 , e –9 , e –16 , … {1 – (1/3) n } { } 1 / 3 , –4 / 9 , 1 / 3 , –16 / 81 , 25 / 243 , … { n 3 /(2 n 3 +1)} {( n 2 + 1)/ n 3 } [Note: the only two things you write in this column should be conv. and div. ] [Note: the only two things you write in this column should be div. and N/A .] Note: i) If lim n →∞ a n = constant, then the sequence converges; if lim n →∞ a n is , – , or DNE, then the sequence diverges. ii) If lim n →∞ a n 0, then the series diverges; if lim n →∞ a n = 0, we can’t tell whether the series converges or diverges, i.e., it’s not applicable.
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Math 155 Exam 3-Sample 2006 - Math 155 Section 02 Calculus...

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