n = 1 18 (−1)”+ ¹ 3 · 7 · 11 · · · (4n − 1)(x − 3)” · - 1)(x-3)" 4n

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%
Find the interval of convergence of the power series. Also include a check for convergence at the endpoints of the interval.
.
33.
(− 1)”+¹ 3 · 7 · 11 · · · (4n − 1)(x − 3)"
•
-
-
4n
11=
Transcribed Image Text:. 33. (− 1)”+¹ 3 · 7 · 11 · · · (4n − 1)(x − 3)" • - - 4n 11=
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question

In this answer to the previous follow-up question, why do we multiply the (4n - 1) at the top? This was one of my previous follow-up questions, and the answer to that was "...no need to write (4n -1) in the top." And it is still confusing me.

Now,
을(-1)+1 3.7.11.
-
(4n-1)(x-3)^
n=1
կո
an =
1-117+1 3.7. 11.
կո
= land =
3.7.11
կո
(4n-1) (x-3)"
(4n-1)/(x-3)^
&lantıl
3. 7. 11.
-
-
4n+1
Σ an (say)
n=1
(4n-1) (4n+3) (x-3)/2+1
Series, Eland converges if
M=1
By Ratio
test
lim lantil
lanl
< 1
L
1.
at lim lantil
1,
test fails.
n-p
1 anl
Now, lim lantil
nto lanl
=
lim
ntoo
37.11.
3.7.11.
-
=) lim lantil
Flim
(4n+3)1x-317+1
ntoo
lanl
7-7700
4n+1
= lim lantıl
n700
Ian'
= lim (4n+3) 1x-31
n200
4
(4n-1) (4n+3) 1x-317+1
4n+1
(49-1) 1x-3/m
կո
x կո
1x-31"
Transcribed Image Text:Now, 을(-1)+1 3.7.11. - (4n-1)(x-3)^ n=1 կո an = 1-117+1 3.7. 11. կո = land = 3.7.11 կո (4n-1) (x-3)" (4n-1)/(x-3)^ &lantıl 3. 7. 11. - - 4n+1 Σ an (say) n=1 (4n-1) (4n+3) (x-3)/2+1 Series, Eland converges if M=1 By Ratio test lim lantil lanl < 1 L 1. at lim lantil 1, test fails. n-p 1 anl Now, lim lantil nto lanl = lim ntoo 37.11. 3.7.11. - =) lim lantil Flim (4n+3)1x-317+1 ntoo lanl 7-7700 4n+1 = lim lantıl n700 Ian' = lim (4n+3) 1x-31 n200 4 (4n-1) (4n+3) 1x-317+1 4n+1 (49-1) 1x-3/m կո x կո 1x-31"
Solution
Bartleby Expert
SEE SOLUTION
Follow-up Question

So I worked out the question. And I got the below setup. And I got the interval of convergence as (-1, 7). But when I checked the back of the book, it said the answer was x = 3. Could anyone help with what I did wrong?

3315
T
307-11---Un-1/x-3)
we enforce the condition of converg
ence of the ratio test
fim 3-7-7-3) (x3)
☑
い 。37 11-441-163
14/4731
41
4 un- 4T
⇒ x 344
Interval of convergenc
Endpoints
TWE
7844
h=|
(-1) 3070/1000 (n-1)/4"
14
diverges
(3.7-11-0
4
diverges
Transcribed Image Text:3315 T 307-11---Un-1/x-3) we enforce the condition of converg ence of the ratio test fim 3-7-7-3) (x3) ☑ い 。37 11-441-163 14/4731 41 4 un- 4T ⇒ x 344 Interval of convergenc Endpoints TWE 7844 h=| (-1) 3070/1000 (n-1)/4" 14 diverges (3.7-11-0 4 diverges
Solution
Bartleby Expert
SEE SOLUTION
Follow-up Question

Why is there an extra (4n - 1) in the top in u(n+1)? 

 

Оли =
(+372
3.7.11 (4nes (4n+3)
(x-3)
4741
7+1
Transcribed Image Text:Оли = (+372 3.7.11 (4nes (4n+3) (x-3) 4741 7+1
Solution
Bartleby Expert
SEE SOLUTION
Similar questions
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,