Test 2 Fall 2006 solutions

Test 2 Fall 2006 solutions - Math 1B First Exam Name:_...

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Math 1B First 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 = Converges by Direct Comparison Test. 2 2 11 n n e < b) 1 ln n n n = Diverges by the Integral test. () 2 1 2 1 1 ln ln | x dx x x = =∞ c) 2 0 1 n n n e = Converges by the Alternating Series Test. d) 1 2 0 n n n e = Converges by the Root Test. 1 22 2 lim lim 1 n nn n ee −− →∞ −= = < e) 1 n n a = where 21 54 2, k k aa a + + == .
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Converges by the Ratio Test: 1 212 lim lim 1 545 n nn n a n an + →∞ →∞ + == < f) 3 24 357 1 ... −+−+ () 1 1 21 n n n a n + =− + . Diverges by the nth term test. g) 4 3 2 0 85 1 n n = ++ Diverges by Limit comparison with 4 3 2 3 2 11 1 n n n ∞∞ = .
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2. Let 1 () n n x fx n = = .
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Test 2 Fall 2006 solutions - Math 1B First Exam Name:_...

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