Use the binomial series to expand the function as a power series. f(x) = 5√/1+ O 5+ n=1 5 5+ x + 18₁ 5 5+ 18 n=0 5 (-1)-¹1.3.5.... (2n − 1) 2nn! n=2 + x² 9 5+5 (-1)" 1.3.5. .... (2n − 3) 2nn! n=2 5 (-1)”+1 2"n! 5(-1)-1 2"n! 72 (-)" - (-)" 72 (5) " 5 (−1)n-¹1.3.-5. .... (2n − 3) . 2"n! Watch It ()* 72 ²¹ (-)" State the radius of convergence, R. (If the radius of convergence is infinity, R = 1/9 Need Help?
Use the binomial series to expand the function as a power series. f(x) = 5√/1+ O 5+ n=1 5 5+ x + 18₁ 5 5+ 18 n=0 5 (-1)-¹1.3.5.... (2n − 1) 2nn! n=2 + x² 9 5+5 (-1)" 1.3.5. .... (2n − 3) 2nn! n=2 5 (-1)”+1 2"n! 5(-1)-1 2"n! 72 (-)" - (-)" 72 (5) " 5 (−1)n-¹1.3.-5. .... (2n − 3) . 2"n! Watch It ()* 72 ²¹ (-)" State the radius of convergence, R. (If the radius of convergence is infinity, R = 1/9 Need Help?
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 binomial series to expand the function as a power series and state the radius of convergence
Transcribed Image Text:Use the binomial series to expand the function as a power series.
f (x) = 5√√/1+ 9
5 + 5 (−1)″−¹ 1 · 3 · 5 · ... · (2n − 1)
.
n=1
5
5+ -x+
18
5
5+ x +
18
7=2
n=0
5 (−1)n+1
2"n!
5(-1)"-1
2"n!
5+5 (-1)"1.3.5....· (2n − 3)
-
2"n!
7=2
72
(5)"
(5)
Watch It
72
− (57)"
5(-1)-¹1.3.5..... (2n - 3)
72
³) (5) "
2"n!
(-)"
State the radius of convergence, R. (If the radius of convergence is infinity, e
R = 1/9
Need Help?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
