e3-sample

# e3-sample - (a ∞ ∑ n =1 cos nπ n 3 4(b ∞ ∑ n =1-1...

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Math 170, Section 01, Exam 3, Sample Saturday, November 14th, 2009 Name (PRINT clearly): You will receive full credit only if you show all work and explain all steps. 1. Write 3 . 417 as a ratio of integers (you do not have to simplify your answer). 2. Find the sum of the series n =1 2 n 2 + 3 n . 3. Test the following series for convergence. (a) n =1 n 2 + n + 1 n 5 + 3 n (b) n =1 1 n 1+1 /n (c) n =1 ne - 4 n 2 4. Decide whether the following series converge conditionally, converge absolutely, or diverge.
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Unformatted text preview: (a) ∞ ∑ n =1 cos( nπ ) n 3 / 4 (b) ∞ ∑ n =1 (-1) n 3 n n ! n n (c) ∞ ∑ n =1 (-1) n n ln( n ) 5. Consider the inﬁnite series 2 5-2 · 6 5 · 8 + 2 · 6 · 10 5 · 8 · 11-2 · 6 · 10 · 14 5 · 8 · 11 · 14- ··· (a) Based on the pattern give a formula for the n th term of the series. (b) Test the series for convergence. 6. Find the values of p for which the following series converges ∞ X n =1 1 n (ln( n )) p . 1...
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## This document was uploaded on 10/29/2011 for the course MATH 170 at Vanderbilt.

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