Use the formula for the binomial series: (1 + x) to obtain the Maclaurin series for 1 - 8x + 1 - 8x + 1 - 8x + 1 + 8x + 1 + 8! 7! 00 ; Σ (−1)k+1 (k + 7)! xk 9! k! k=2 00 k=1 00 Σ(−1)k (k+9)! x + k! k=2 1 77 2 (-1)^ (k+ 7)! k! k=2 k=2 Σ(k+7)! (k + 8)! k! +4 (1 + x)8 xk = = -xk 1 + mx + 1 + E k=1 m(m-1) 2! -x² + + -xk ... m(m-1)(m-k+l) k! m(m-I)…(m-k+I)xit k! |x| < 1 if ...
Use the formula for the binomial series: (1 + x) to obtain the Maclaurin series for 1 - 8x + 1 - 8x + 1 - 8x + 1 + 8x + 1 + 8! 7! 00 ; Σ (−1)k+1 (k + 7)! xk 9! k! k=2 00 k=1 00 Σ(−1)k (k+9)! x + k! k=2 1 77 2 (-1)^ (k+ 7)! k! k=2 k=2 Σ(k+7)! (k + 8)! k! +4 (1 + x)8 xk = = -xk 1 + mx + 1 + E k=1 m(m-1) 2! -x² + + -xk ... m(m-1)(m-k+l) k! m(m-I)…(m-k+I)xit k! |x| < 1 if ...
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 44E
Related questions
Question
![Use the formula for the binomial series:
to obtain the Maclaurin series for
1 – 8x +
1 - 8x +
1 – 8x +
1+
9/
8!
1
71
100
Σ
Σ+1+ (k + 7)!
k
k=2
1 + 8x + Σ Σ + 7
(k + 7)!
k!
k=1
(−1)k (k + 9)!
7!
Σ
xk
k!
k=2
(−1)k
(1 + x) =
(k + 8)!
k!
1
(1 + x)8
xk
-xk
(k + 7)!
k!
-xk
xk
1 + mx +
1+
1 + 2
Σ
100
=1
m(m-1) x2 +
m(m-1)...(m-k+1)
...
+
xk
m(m-1)-(m-k+D)
if
[x] < 1
Β](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F97ca65a2-275b-43b9-9da8-8ff8b69b5c25%2F9bb0a3f2-94be-42c6-ab3b-a8ce501e6ba1%2F95otgxm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Use the formula for the binomial series:
to obtain the Maclaurin series for
1 – 8x +
1 - 8x +
1 – 8x +
1+
9/
8!
1
71
100
Σ
Σ+1+ (k + 7)!
k
k=2
1 + 8x + Σ Σ + 7
(k + 7)!
k!
k=1
(−1)k (k + 9)!
7!
Σ
xk
k!
k=2
(−1)k
(1 + x) =
(k + 8)!
k!
1
(1 + x)8
xk
-xk
(k + 7)!
k!
-xk
xk
1 + mx +
1+
1 + 2
Σ
100
=1
m(m-1) x2 +
m(m-1)...(m-k+1)
...
+
xk
m(m-1)-(m-k+D)
if
[x] < 1
Β
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage