Answered: 4. The series f(x) = ² - can be shown… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.3: Geometric Sequences

Problem 49E

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4.
00
n
The series f(x) = - can be shown to converge on the interval [-1, 1).
n
n=1
(a)
Find the series f'(x) in series form and find its interval of convergence,
showing all work and reasoning, of course!
(b)
Find the series f(x) dx in series form and find its interval of
convergence, showing all work, of course!

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4. The series f(x) = can be shown to converge on the interval [-1, 1). n=1 n (a) Find the series f'(x) in series form and find its interval of convergence, showing all work, of course! (b) Find the series [ f(x)dx in series form and find its interval of convergence, showing all work, of course!
The function f is defined by the power series x7 X f(x) = X 3 5 7 for all real number X for which the series converges. (a) Find the interval of convergence of the power series for f Justify your answer. (b) Write the first four nonzero terms and the general term for an infinite series that represents f'(x) + + (-1)"x2n+1 2n + 1
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sot agovno Find all numbers x for which the power series (A) 3'3 converges. 3k k=0 1912 (B) [-1, 1] (C) (-3, 3) (D) [-3,3]
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