01 Midterm-Sample

# 01 Midterm-Sample - =2 2 1 2 n& 1 2 n 1(a(10 points Find...

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University of California, Riverside Department of Mathematics Midterm Mathematics 9C - First Year of Calculus Sample 1 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) Does the following sequence converge or diverge? If the justify your answers! a n = ln n n P 1 n

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Unformatted text preview: =2 2( 1 2 n & 1 2 n +1 ) : (a) (10 points) Find an expression for the n th partial sum s n of the series. (b) (10 points) Compute lim n !1 s n : 3. (20 points) Determine whether the following series converges absolutely, conditionally or whether it diverges. Be sure to justify your answers! 1 X n =1 ( & 1) n n 4. (20 points) Determine the convergence or divergence of the following series. Be sure to justify your answer! 1 X n =1 1 n 2 3 n 1 5. Find the radius of convergence and the interval of convergence of the series. (a) (10 points) P 1 n =0 p nx n (b) (10 points) P 1 n =0 ( & 1) n ( x & 3) n 2 n +1 2...
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01 Midterm-Sample - =2 2 1 2 n& 1 2 n 1(a(10 points Find...

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