227seriesHWonDipoles

227seriesHWonDipoles - Math 227 Sections 4 and 5 Written HW...

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Math 227 Sections 4 and 5 Written HW 12 due Friday 4/22 Some exercises and applications with power series 1. Start with the geometric series 1 1 x = 1 X n =0 x n (valid for 1 < x < 1 ). f ( x ) = 1 (1 x ) 2 : (b) Test your answer by substituting in the value x = 0 : 1 terms. The sum should be fairly close to 1 = (1 & 0 : 1) 2 = 1 : 234 567 901 : (c) Try the same thing using x = 0 : 5 : approximation of 1 = (1 & 0 : 5) 2 = 4 : 00000 : What is the reason for this? (Look at the terms you are of the series you are omitting.) 20 terms of the series using x = 0 : 5 : Answer: 3 : 999 958 038 . 2. Replace x by x in your series for f ( x ) to obtain a series for g ( x ) = 1 (1+ x ) 2 : The next exercise uses
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