(b) If m < a1 + ... + an < M n, and v, is positive and + anVn < Mv1. + anUn| < Mvi Vn. decreasing, then mvị < ajvi + ... (c) If in (b) |Sn| < M Vn, then |a1v1 + ... + anVn| < Mv1 Vn.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
icon
Related questions
Question
100%

Prove theorem 5b and 5c.

Advanced Calculus II
Infinite Series
The Abel and Dirichlet Tests.
Theorem 5. Abel's Lemma, or Partial Summation
Given Sn =
= aj + a2+
+ An
...
81(v1 – v2) +...+ Sn-1(Vn-1– Vn) +8nVn
(6) If m < a1+... + an < M Vn, and v,n is positive and
... + a,Vn < Mv1.
(a) a1v1 +...+a,Vn
decreasing, then mvị < ajvị +
(c) If in (b) |Sn| < M \n, then |a1v1 + ... + anVn|< Mv1 Vn.
Transcribed Image Text:Advanced Calculus II Infinite Series The Abel and Dirichlet Tests. Theorem 5. Abel's Lemma, or Partial Summation Given Sn = = aj + a2+ + An ... 81(v1 – v2) +...+ Sn-1(Vn-1– Vn) +8nVn (6) If m < a1+... + an < M Vn, and v,n is positive and ... + a,Vn < Mv1. (a) a1v1 +...+a,Vn decreasing, then mvị < ajvị + (c) If in (b) |Sn| < M \n, then |a1v1 + ... + anVn|< Mv1 Vn.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage