(a)Determine the first five terms of Taylor series for xe" about x=1.(ii)Differentiate the Taylor series for xe* , and use the result to show thatk+1f'(x) = eE*(r – 1)*1(k – 1)!(b)Determine whether the following series are convergent or not using the ratio test;7"En$ 2* (n+ 1)(ii)n!n=1(iii)7n!n=1

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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.3: Geometric Sequences

Problem 44E

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Determine the first five terms of Taylor series for xe" about x=1. (ii) Differentiate the Taylor series for xe" , and use the result to show that k+1 f'(x) = eE E (k – 1)!