A sequence ₁,₂... is such that u, = -r-1 (i) (ii) n Show that Σ r=2 11+5 Hence find Σ r=8 =2_n+1 n! r-3r+1 (r-1)! convergent. r=2 - 11-00 r! and u, = in terms of n. = U₁_2 + Limit Comparison test states that for two series of the form a, and Σb, with r=k r=k r+1-² 80 a,b,≥0 for all n, if lim">0, then both Σa, and b, converges or both diverges b₁ r=k r=k when r≥ 2. -r-1 (iii) Given that ¹²- is convergent, using the test, explain why r! r=2 r-2 (r-1)! is
A sequence ₁,₂... is such that u, = -r-1 (i) (ii) n Show that Σ r=2 11+5 Hence find Σ r=8 =2_n+1 n! r-3r+1 (r-1)! convergent. r=2 - 11-00 r! and u, = in terms of n. = U₁_2 + Limit Comparison test states that for two series of the form a, and Σb, with r=k r=k r+1-² 80 a,b,≥0 for all n, if lim">0, then both Σa, and b, converges or both diverges b₁ r=k r=k when r≥ 2. -r-1 (iii) Given that ¹²- is convergent, using the test, explain why r! r=2 r-2 (r-1)! is
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
Transcribed Image Text:1
A sequence u,₁,U₂... is such that u, =
r!
(i)
(ii)
Show that
n
r=2
11+5
Hence find Σ
(iii) Given that
convergent.
r² -r-1
r!
r=2
r²-3r+1
= 2
8(r-1)!
²-
n+1
n!
r!
and u = U_2 +
r-2
Limit Comparison test states that for two series of the form a, and b, with
r=k
r=k
in terms of n.
a₁
a,b 20 for all n, if lim- ->0, then both Σa, and b, converges or both diverges
11-8
b.
11
r=k
r=k
r+1-r²
r!
11
when /> 2.
-1
is convergent, using the test, explain why
r-2
(r-1)!
is
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 3 steps with 3 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,
