Find the radius of convergence, R, of the series. 00 n = 3 +7 +6 6n! Find the interval, I, of convergence of the series. (Enter your answer using interval notation.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
100%

sum n = 3 to infinity (X ^ (n+6))/(6*n!)

Find the radius of convergence, R, of the series.
n = 3
Find the interval, I, of convergence of the series. (Enter your answer using interval notation.)
lim
n→ co
00
Step 1
We will use the Ratio Test to determine the radius of convergence.
We have the following.
Step 2
+7 +6
6n!
an +1
an
lim
n→ ∞
=
=
Simplifying, we get lim
n→ ∞0
lim
n→ ∞0
=
||
lim
n→∞⁰ 6(n + 1)!
Step 3
Therefore, we now have the following.
an+ 1
a
+7+7
6(n + 1)!
+ 6
6n!
+7+7 6
Ix lim
= |x|.
n+1
1
n→ ∞⁰ n + 1
X
n!
+7+6
n+1
n!
Transcribed Image Text:Find the radius of convergence, R, of the series. n = 3 Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) lim n→ co 00 Step 1 We will use the Ratio Test to determine the radius of convergence. We have the following. Step 2 +7 +6 6n! an +1 an lim n→ ∞ = = Simplifying, we get lim n→ ∞0 lim n→ ∞0 = || lim n→∞⁰ 6(n + 1)! Step 3 Therefore, we now have the following. an+ 1 a +7+7 6(n + 1)! + 6 6n! +7+7 6 Ix lim = |x|. n+1 1 n→ ∞⁰ n + 1 X n! +7+6 n+1 n!
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,