M138.assn7.W07 - MATH 138 Assignment 7(1 page Winter 2007...

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Unformatted text preview: MATH 138 Assignment 7 (1 page) Winter 2007 Submit ALL problems (except 4. c)) by 8:20 a.m. Friday, March 9 1. For each series apply the 71"“ Term Test and hence state whether the. diverges, or might converge. n+1 )Zn— b) 2:1+3" C) Zl+e]/" )2 \/r—I.n—1 C) annn 1'12: 11:0 3 71:1 71:2 11:2 2. For each series in problem 1 which you found might converge, apply the Integral Test or the Comparison Test to determine whether the series converges or diverges. n2 3 Use the Compaiison Test to show that the series 2( — converges. (n +1)! r1: 1 0011171 4. a) Use the Integral Test to show the series — converges 11:2 13) Apply the Corollary to the Integral Test (page 86 of Course Notes, or text page 727) to determine an upper bound for the error if the series in a) is approximated by 5'50. (DO NOT find 550.) 1X: . . lnn C) (Optional) Determine all values of p such that —p converges. 71 11:2 0° 1' 2 r ‘ sin n . _ _ , . . a. a) Show that E 1 + n is convergent by comparing to a suitable geou‘ietric series. 7r , 71:1 b) Find an upper bound on the error if 54 is used to approximate the sum of the series in a). 6. By comparison to an appropriate p—series determine whether each series converges or diverges. OO 1 arctan( ()n n —— l a) 2 b) 2 3 2 C) 2 4 A 11:2 fl — 1 11:1 n —/— ‘n.=2 TL + 1 CC 1 7. a) Find the partial Sum SN of the series 2 by using partial fractions. Hence show (n +1)(-n + 2) 72:1 1 that the series converges to 5 b) Criticize the following calculation, in which adjacent terms are cancelled indefinitely. 00 00 1 __—‘ —n. n+1)_(1 2) (2 3) (3 4) _1 ;(n+1)(n+2)—”2=4<n+1+71+2 _ 2+3 + 3+4 4 4+5 + _ 2‘ This illustrates that we cannot treat series as finite sums. ...
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