03 Midterm-Sample

# 03 Midterm-Sample - (a(10 points 1 2& 1 2 ± 3 1 2 ± 3...

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University of California, Riverside Department of Mathematics Midterm Mathematics 9C - First Year of Calculus Sample 3 Instructions: This exam has a total of 100 points. You have 50 minutes. You must show all your work to receive full credit You may use any result done in class. The points attached to each problem are indicated beside the problem. You are not allowed books, notes, or calculators. Answers should be written as p 2 as opposed to 1 : 4142135 ::: . 1. (20 points) Test if the following sequence f a n g converges or diverges. If it converges, also °nd the limit of the sequence. a n = ° n ° 7 n ± 1 n 2. For each the following series °nd the sum, if it converges. If you think it diverges explain why. (a) (10 points)

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Unformatted text preview: (a) (10 points) 1 2 & 1 2 ± 3 + 1 2 ± 3 2 & 1 2 ± 3 3 + 1 2 ± 3 4 & 1 2 ± 3 5 + ±±± (b) (10 points) 1 X n =1 3 (2 n & 1)(2 n + 1) 3. Test if each the following series converges or diverges. Give reasons and clearly state if you are using any standard test. (a) (10 points) 1 X n =1 n ! (3 n + 1)! 1 (b) (10 points) 1 X n =2 p n n 2 & 3 4. Test the series for convergence or divergence. (a) (10 points) P 1 n =1 ( & 1) n sin & n (b) (10 points) P 1 n =1 ( & 1) n cos & n 5. Find the radius of convergence and the interval of convergence of the series. (a) (10 points) P 1 n =0 ( & 1) n x n n +1 (b) (10 points) P 1 n =0 ( x +1) n n 2 2...
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