Expand the given function in a Maclaurin series. f(z) = e-5z 00 k = 0 5K (-1)K. K! R = ∞ X Give the radius of convergence R of the series.
Expand the given function in a Maclaurin series. f(z) = e-5z 00 k = 0 5K (-1)K. K! R = ∞ X Give the radius of convergence R of the series.
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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Transcribed Image Text:Expand the given function in a Maclaurin series.
f(z) = e-5z
Σ((-1)*.
(−1)².
k = 0
54
K!
R =
X
Give the radius of convergence R of the series.
![where
ак
KI
Now if Z₁ =0,
machawen series..
So the maclawrin series is 2 +K(0)
K= K₂
Now here
So from (1), we get
Ž KO
•Z^
2 *
K=0
Now
6:23 pm
'f'(Z) = -50-52
f" (Z) = (-5).(-5) (-57-
f" (Z) = -125 e -5Z
fk (0) K
KI
Step3
c)
K=
∞
2 fK (0) ₂K = 1-√√√2 + 5/1/2
Z
K=0
then the series is called
K-400
Tim akti
ak
Z+
21
= f ° (0) + f(1/2 Z+ + + + " (0) 2²7.
[Hoef"= £²]
Z₁ = 1-52+ 25 Z² = 125 2³ +
This is the Maclawin Series.
Now the n-th term of this series is
ak = (-1)k 5k"
K!
=156-52
AC 51%
Y 5
J
3!
KH
lim (-1) K+K+) K!
K∞ (K+1)]
LX
2²³+
(1) K5k
Do
8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96b6da5a-a741-4733-bd63-c5fba54e8042%2Fa3ed06db-453a-41d2-bc1f-a1a43901ee27%2F3tbdnu6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:where
ак
KI
Now if Z₁ =0,
machawen series..
So the maclawrin series is 2 +K(0)
K= K₂
Now here
So from (1), we get
Ž KO
•Z^
2 *
K=0
Now
6:23 pm
'f'(Z) = -50-52
f" (Z) = (-5).(-5) (-57-
f" (Z) = -125 e -5Z
fk (0) K
KI
Step3
c)
K=
∞
2 fK (0) ₂K = 1-√√√2 + 5/1/2
Z
K=0
then the series is called
K-400
Tim akti
ak
Z+
21
= f ° (0) + f(1/2 Z+ + + + " (0) 2²7.
[Hoef"= £²]
Z₁ = 1-52+ 25 Z² = 125 2³ +
This is the Maclawin Series.
Now the n-th term of this series is
ak = (-1)k 5k"
K!
=156-52
AC 51%
Y 5
J
3!
KH
lim (-1) K+K+) K!
K∞ (K+1)]
LX
2²³+
(1) K5k
Do
8
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