Expand the given function in a Maclaurin series. 1 (1 + 9z)² k = 1 f(z) = eBook (-1)(-2-1)--(-2-(k-2)) (k-1)! Give the radius of convergence R of the series. 1 9 X
Expand the given function in a Maclaurin series. 1 (1 + 9z)² k = 1 f(z) = eBook (-1)(-2-1)--(-2-(k-2)) (k-1)! Give the radius of convergence R of the series. 1 9 X
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.4: Complex And Rational Zeros Of Polynomials
Problem 15E
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Transcribed Image Text:Step2
b)
te) =
E
-
(1+97) 2
of
Σ (-²1) (-2-1) (2-2) - - (-1- (2-1)
n=1
n!
1+
00
Σan (17)"
n=0
NOW as
you
t(t) =
C
C
00
K=1
O
248
pradius of convergence,
1
On
R
lim
tim
nye
6:08 pm
6
Where
and
the expression.
fon
an
R.
(n+1)
a₁ = (-1) (-1-1)-(-2-(^-^)) ₁
n!
for 321
G
акі
K=1,
(-2)(1)-(-1-n)
(n+1)!
(-2)(-2-¹)--(-2-(K-2))
(K+)!
91
AO 48%
n!
√x
for k²2.
(-2) (-2-1)--(-2-(-1))
Do
Transcribed Image Text:Expand the given function in a Maclaurin series.
k = 1
f(z) =
eBook
1
(1 + 9z)²
(-1)(-2-1)--(-2-(k-2))
(k-1)!
Give the radius of convergence R of the series.
1
9
X
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