Find the Maclaurin series of the function. f(x) = In (1 – 4x) Choose the Maclaurin series. 00 !"x" In (1 – 4x) : n=1 00 In (1 – 4x) = 5 (-1)"-'4"x" n n=1 00 4" x" In (1 – 4x) : 4n n=1 00 -14n In (1 – 4x) = 4n n=1 Identify the interval on which the series is valid. (Give your answer as an interval in the form (*, *). Use the symbol co for infinity, U for combining intervals, and an appropriate type of parenthesis "(",")", "L","]" depending on whether the interval is open or closed. Enter Ø if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.) The expansion is valid for:
Find the Maclaurin series of the function. f(x) = In (1 – 4x) Choose the Maclaurin series. 00 !"x" In (1 – 4x) : n=1 00 In (1 – 4x) = 5 (-1)"-'4"x" n n=1 00 4" x" In (1 – 4x) : 4n n=1 00 -14n In (1 – 4x) = 4n n=1 Identify the interval on which the series is valid. (Give your answer as an interval in the form (*, *). Use the symbol co for infinity, U for combining intervals, and an appropriate type of parenthesis "(",")", "L","]" depending on whether the interval is open or closed. Enter Ø if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.) The expansion is valid for:
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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Please solve the second question
![Find the Maclaurin series of the function.
f(x) = In (1 – 4x)
Choose the Maclaurin series.
In (1 – 4x) = -
n=1
-1)"-14"x"
In (1 – 4x) =
n=1
4" x"
In (1 – 4x) = -
4n
n=1
00
(-1)"-1x4"
In (1 – 4x) =
4n
n=1
Identify the interval on which the series is valid.
(Give your answer as an interval in the form (*, *). Use the symbol o for infinity, U for combining intervals, and an appropriate
type of parenthesis "(",")", "[","]" depending on whether the interval is open or closed. Enter Ø if the interval is empty. Express
numbers in exact form. Use symbolic notation and fractions where needed.)
The expansion is valid for:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F073e7bc6-80b4-4c2f-9d26-9aea71c9721c%2Fcd72704f-ef7f-4cca-af6c-c641ed065b5f%2F3ru1a4j_processed.png&w=3840&q=75)
Transcribed Image Text:Find the Maclaurin series of the function.
f(x) = In (1 – 4x)
Choose the Maclaurin series.
In (1 – 4x) = -
n=1
-1)"-14"x"
In (1 – 4x) =
n=1
4" x"
In (1 – 4x) = -
4n
n=1
00
(-1)"-1x4"
In (1 – 4x) =
4n
n=1
Identify the interval on which the series is valid.
(Give your answer as an interval in the form (*, *). Use the symbol o for infinity, U for combining intervals, and an appropriate
type of parenthesis "(",")", "[","]" depending on whether the interval is open or closed. Enter Ø if the interval is empty. Express
numbers in exact form. Use symbolic notation and fractions where needed.)
The expansion is valid for:
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