Test 2 Fall 2006 _short_ - Math 1B Second Exam Name:_ SID:_...

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Math 1B Second Exam Name:_________________________ SID:_____________________ (last, first) 1. For each of the series below, determine whether it converges or diverges. Use each of the following tests exactly once: n th term test, integral test, direct comparison test, limit comparison test, alternating series test, ratio test, and root test. Please indicate which test you used on which part. (10 points for each part) a) 2 0 n n e = b) 1 ln n n n = c) () 2 0 1 n n n e = d) 1 2 0 n n n e = e) 1 n n a = where 21 11 54 2, k nn k aa a + + == . f) 3 24 357 1 ... −+−+ g) 4 3 2 0 85 1 n n = ++ For each test listed below, which problem did you use that test for? n th term test: direct comparison test: alternating series test: integral test: limit comparison test: ratio test: root test:
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2. Let 1 () n n x fx n = = . a) Find the power series representation for f x and find its interval of convergence.
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This note was uploaded on 04/03/2008 for the course MATH 1B taught by Professor Reshetiken during the Spring '08 term at University of California, Berkeley.

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Test 2 Fall 2006 _short_ - Math 1B Second Exam Name:_ SID:_...

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