final2sols - Name UCLA ID Number Section letter Math 31b Integration and Innite Series Final Exam Instructor Ciprian Manolescu Winter 2013 You have 3

# final2sols - Name UCLA ID Number Section letter Math 31b...

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Name: UCLA ID Number: Section letter: Math 31b : Integration and Infinite Series Final Exam Instructor: Ciprian Manolescu Winter 2013 You have 3 hours. No books, notes or calculators are allowed. Do not use your own scratch paper.
1.Multiple Choice.(2 points each) Circle the correct answer.You do not need tojustify your answer, and no partial credit will be given.(i) The infinite seriesXn=012nn! (a) converges toe2(b)converges toe1/2(c) converges to 2(d) diverges to infinity(e) None of the above. (ii) The interval of convergence of the power seriesn!(x-1)nis X n =1 (iii) If{an}is a divergent sequence, then:
(iv) For 0< p <1, the alternatingp-series X n =1 ( - 1) n n p (v) If{an}is a sequence of positive numbers such that limn→∞an= 0, thenXn=1 (a)(-1)nanmust converge absolutely(b)Xn=1(-1)nanmust converge conditionally(c)Xn=1(-1)nanmust converge, but we can’t say if it does so absolutely or conditionally(d)Xn=1(-1)nanmust diverge(e)Xn=1(-1)nanmay converge or diverge.