(-1)"4"+1µn+1 3n+1(n + 1) In this problem, we investigate the power series n=0 (-1)"4"+1pn+1 3n+1(n + 1) (-1)"4"+1µn+5 (c) If we multiply the series by x we get x -, a re- 3n+1(n + 1) n=0 n=0 4x lated power series, which is equal to xª ln (+1) on the same interval you identified in part b. Express /2* in ( +1) dx as a power series in x. (4x (d) Let g(x) = xª In + Find g'(x), and the Maclaurin series for g'(x). %3D Consider, but do not give a response to the question: should you find the Maclaurin series for g'(x) directly, or by starting from the series in (c)?
(-1)"4"+1µn+1 3n+1(n + 1) In this problem, we investigate the power series n=0 (-1)"4"+1pn+1 3n+1(n + 1) (-1)"4"+1µn+5 (c) If we multiply the series by x we get x -, a re- 3n+1(n + 1) n=0 n=0 4x lated power series, which is equal to xª ln (+1) on the same interval you identified in part b. Express /2* in ( +1) dx as a power series in x. (4x (d) Let g(x) = xª In + Find g'(x), and the Maclaurin series for g'(x). %3D Consider, but do not give a response to the question: should you find the Maclaurin series for g'(x) directly, or by starting from the series in (c)?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
Related questions
Question
Transcribed Image Text:(-1)"4"+1µn+1
3n+1(n + 1)
In this problem, we investigate the power series
n=0
(-1)"4"+1pn+1
3n+1(n + 1)
(-1)"4"+1µn+5
(c) If we multiply the series by x we get x
-, a re-
3n+1(n + 1)
n=0
n=0
4x
lated power series, which is equal to xª ln
(+1)
on the same interval you identified
in part b.
Express /2* in (
+1) dx as a power series in x.
(4x
(d) Let g(x) = xª In
+
Find g'(x), and the Maclaurin series for g'(x).
%3D
Consider, but do not give a response to the question: should you find the Maclaurin series
for g'(x) directly, or by starting from the series in (c)?
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