Use the formula for the binomial series: (1 + x)" = = to obtain the Maclaurin series for (k + 7)! 1 + 8x + Σ k! k=2 1+ Σ (k + 8)! k! 8! 00 1 - 8x + 9! Σ(-1)+1 + 7! (+7 k! k=2 00 1 1 - 8x + Σ+1+7! 7! k! k=2 00 1 – 8x + k Σ (1) + 9! k! k=2 00 |- 1 (1 + x)8' με 1 + mx + έχ2 + ... + m(m-1) 2! m(m-1)...(m-k+1) k! 1+ Σκι m(m-1).(m-k+1) k! [x] < 1 exk if ark +
Use the formula for the binomial series: (1 + x)" = = to obtain the Maclaurin series for (k + 7)! 1 + 8x + Σ k! k=2 1+ Σ (k + 8)! k! 8! 00 1 - 8x + 9! Σ(-1)+1 + 7! (+7 k! k=2 00 1 1 - 8x + Σ+1+7! 7! k! k=2 00 1 – 8x + k Σ (1) + 9! k! k=2 00 |- 1 (1 + x)8' με 1 + mx + έχ2 + ... + m(m-1) 2! m(m-1)...(m-k+1) k! 1+ Σκι m(m-1).(m-k+1) k! [x] < 1 exk if ark +
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Use the formula for the binomial series:
(1 + x) =
=
to obtain the Maclaurin series for
(k + 7)!
1 + 8x + Σ k!
k=2
00
1+ Σ
(k + 8)!
k!
8!
00
1 - 8x +
Σ(-1)*+1 + 7!
9!
k!
k=2
1
1 - 8x +
Σ+1 +7
7!
k=2
00
1
1 – 8x +
k
Σ (1) + 9!
k!
k=2
1
(1 + x) 8°
1 + mx +
1+ Σκι
m(m-1)
2!
m(m-1)...(m-k+1)
k!
έχω + ... +
m(m-1).(m-k+1)
k!
[x] < 1
exk if
ark
+](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd99741e6-a997-4e6c-a4b1-50ef47327248%2F7d8f4b1f-5086-456f-9124-30130adbbdf1%2Fog86ycl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Use the formula for the binomial series:
(1 + x) =
=
to obtain the Maclaurin series for
(k + 7)!
1 + 8x + Σ k!
k=2
00
1+ Σ
(k + 8)!
k!
8!
00
1 - 8x +
Σ(-1)*+1 + 7!
9!
k!
k=2
1
1 - 8x +
Σ+1 +7
7!
k=2
00
1
1 – 8x +
k
Σ (1) + 9!
k!
k=2
1
(1 + x) 8°
1 + mx +
1+ Σκι
m(m-1)
2!
m(m-1)...(m-k+1)
k!
έχω + ... +
m(m-1).(m-k+1)
k!
[x] < 1
exk if
ark
+
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