(c) If in (b) |sn < M Vn, then |a1v1 + ... + a„Vn| < Mv1 Vn.

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

Prove (c)

Theorem 5. Abel's Lemma, or Partial Summation
Given Sn
ai + a2 +
+ an
...
(a) a1v1+...+anVn = 81(v1 – V2)+...+8n-1(Vn-1– Vn)+SnVn
(b) If m < ai+
decreasing, then mvi < a¡v1 +
(c) If in (b) |sn|< M Vn, then |a1v1 + ... + an Vn| < Mv1 Vn.
|
... + an < M Vn, and v, is positive and
... + a„Vn < Mv1.
Transcribed Image Text:Theorem 5. Abel's Lemma, or Partial Summation Given Sn ai + a2 + + an ... (a) a1v1+...+anVn = 81(v1 – V2)+...+8n-1(Vn-1– Vn)+SnVn (b) If m < ai+ decreasing, then mvi < a¡v1 + (c) If in (b) |sn|< M Vn, then |a1v1 + ... + an Vn| < Mv1 Vn. | ... + an < M Vn, and v, is positive and ... + a„Vn < Mv1.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
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,