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by: Joanne Bergnaum


Joanne Bergnaum
GPA 3.56


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Class Notes
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This 3 page Class Notes was uploaded by Joanne Bergnaum on Saturday September 12, 2015. The Class Notes belongs to MATH 2260 at University of Georgia taught by Rothstein in Fall. Since its upload, it has received 40 views. For similar materials see /class/202072/math-2260-university-of-georgia in Mathematics (M) at University of Georgia.


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Date Created: 09/12/15
Math 2260 Practice Problems November 15 2011 1 Let an n 0 12 be a sequence i What is meant by successive ratios of the sequence ii Say what is means for the sequence to be geometric iii What is meant by nth partial sum of the sequence iv If the sequence is geometric with successive ratios equal to a number r what is the formula for the nth partial sum 2 i State the two properties required of the sequence an such that one may apply the integral test to the series Z an n0 ii Draw a picture that proves the integral test and provide a brief explanation 3 State the ratio test 0 4 The comparison test states that if 0 lt an lt bn and an converges then n0 X Z an also converges Use the comparison test to prove the following statement n0 If there are positive constants cl and 02 such that for all n a 0ltclltilt02 b x x x x then either both series Z bn and Z an converge or both series Z bn and 2 an n0 n0 n0 n0 diverge77 5 What is meant by the term p series For which values of p does a p series converge 6 Say what is means for the sequence an to be alternating X i State the three properties required of the sequence such that the series Z an n0 satis es the alternating series test ii For each of the three properties listed in part ii give an example of a divergent X series Z an that satis es the other two properties n0 1 2 gt0 7 What does it mean for a series Z an to converge absolutely n0 8 The following statement is false 00 If the sequence an converges to 0 then the series 2 an converges77 n0 i Give an example that shows the statement to be false ii Rearrange the words to make a true statement V L 9 Compute 273Ve2l Notice that this is a nite sum i0 10 For each of the following series determine whether the series converges absolutely converges conditionally or diverges Give a brief justi cation i 00 71 ii 00 1 m 00 74 iv 00 74 annn 2 lnn Znlnn2 Zn2lnn n3 n3 n3 11 For each of the following series determine whether the series converges Give a brief justi cation 1 H 1 1 1 i v3 n3x 1 Z 11 Z 1 Zlt tfoogt IV 57 V Z M 3 7 n1 n1 n1 n1 i i 2n n 12 Find the radius of convergence S We 71 n1 13 Find the interval of convergence lt71gtWltz7gtn u WM 1 Z ltngtlt2ngt Z n2 n1 1 n 14 i Check that the power series 271 x2quot is a geometric series n0 ii Compute the series from part i Then using what you know about integration and differentiation of power series nd a power series expression for each of the following functions iii arctana iv Hi2 I 39 39c m mi JYMJF Wm 6 UN w 50 lt13 s was if a we mower TM ML H i W vh m 2 L The Ac 4 PM g f S M a efw MU Jr 39 e


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