Use the formula for the binomial series: (1 + x)" = 1+ mx + ² + … + m(m-1). m(m-1)--(m-k+1), + %3D ... 2! k! 1+2k=1 m(m-1)(m-k+1) if k! |x| < 1 %3D 1 to obtain the Maclaurin series for (1+x)° (k +9)! 1 + 9! k=D1 k! 1 1-9x + (-D(k+10)! 8! k=2 k! (k + 8)! 1+9x+ k! k=2 1 – 9x + E(-1y& + 8) 1- 9x +
Use the formula for the binomial series: (1 + x)" = 1+ mx + ² + … + m(m-1). m(m-1)--(m-k+1), + %3D ... 2! k! 1+2k=1 m(m-1)(m-k+1) if k! |x| < 1 %3D 1 to obtain the Maclaurin series for (1+x)° (k +9)! 1 + 9! k=D1 k! 1 1-9x + (-D(k+10)! 8! k=2 k! (k + 8)! 1+9x+ k! k=2 1 – 9x + E(-1y& + 8) 1- 9x +
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
2
Transcribed Image Text:Use the formula for the binomial series:
m(m-1)--(m-k+1),k + ...
(1 + x)" =
1+ mx + x + ..+
m(m-1)
2!
k!
1+ 5
m(m-1):(m-k+1)*
if
I지 < 1
k!
to obtain the Maclaurin series for
(1 + x)°
5(k + 9)!
1
1 +
9!
k=1
k!
1- 9x +
8!
k=2
k!
(k + 8)!
1+ 9x +
k!
k=2
1- 9x +
(k + 8)!
(-1)
12
13)
1s
18 D
Ho2
%23
24
%
2
3.
4.
5.
6.
To
E
R.
T
Y
A
H
V
alt
LL
Transcribed Image Text:1
to obtain the Maclaurin series for
(1 + x)°
(k + 9)!
9/ 2
1+
k!
k=D1
1- 9x + -1)(k+ 10)!
8!
k=2
k!
(k + 8)!
1+9x +
k!
k=2
1- 9x +
(k + 8)!
(-,
8!
k=2
k!
1- 9x +
10!
k=2
k!
13)
foL
『7 回
19A
ho2
%23
2.
24
4.
6.
Q
R.
Y
A
D
V.
alt
00
CO
5
LL
C3
3.
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