02 Midterm-Sample

02 Midterm-Sample - 1 X n =1 3 n n 3. Determine convergence...

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University of California, Riverside Department of Mathematics Midterm Mathematics 9C - First Year of Calculus Sample 2 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. Evaluate: (a) (10 points) lim n !1 1 ( n 4 n ) n (b) (10 points) P 1 n =1 1 2 1 4 ± n 1 2. (20 points) Determine convergence or divergence:
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Unformatted text preview: 1 X n =1 3 n n 3. Determine convergence or divergence: (a) (10 points) 1 X n =1 ( & 1) n r 1 n (b) (10 points) 1 X n =1 ( & 2) n n ! n n 4. Find the radius of convergence and the interval of convergence of the series. 1 (a) (10 points) P 1 n =0 n n x n (b) (10 points) P 1 n =0 ( x +1) n p n 5. If P 1 n =0 c n x n converges, does it follow that the following series con-verges? (a) (10 points) P 1 n =0 c n & x 2 n (b) (10 points) P 1 n =0 c n ( & x ) n 2...
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02 Midterm-Sample - 1 X n =1 3 n n 3. Determine convergence...

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