Explain the focus and reasons for establishment of 12.5.3 about alternating series. and explain the reason why (sigma k=1 to infinite)(-1)k+1/k = 1/1 - 1/2 + 1/3 - 1/4 + .... converges. 12.5.3 THE BASIC THEOREM ON ALTERNATING SERIESLet a0, a1, a2, be a decreasing sequence of positive numbers. The series-ao a₁a2 — a3 + ·-=Σ(-1)^akk=0iffconvergesак0

Answered: 12.5.3 THE BASIC THEOREM ON ALTERNATING…

12.5.3 THE BASIC THEOREM ON ALTERNATING SERIES Let a0, a1, a2, be a decreasing sequence of positive numbers. The series - ao a₁a2 — a3 + · - = Σ(-1)^ak k=0 iff converges ак 0

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.3: Geometric Sequences

Problem 49E

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Question

Explain the focus and reasons for establishment of 12.5.3 about alternating series. and explain the reason why (sigma k=1 to infinite)(-1)^k+1/k = 1/1 - 1/2 + 1/3 - 1/4 + .... converges.

12.5.3 THE BASIC THEOREM ON ALTERNATING SERIES
Let a0, a1, a2, be a decreasing sequence of positive numbers. The series
-
ao a₁a2 — a3 + ·
-
=
Σ(-1)^ak
k=0
iff
converges
ак
0

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