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Find an alternating series which converges but such that the Alternat- ing Series Test does not apply.

Find an alternating series which converges but such that the Alternat- ing Series Test does not apply.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Real Analysis II: Solve the problem in photo 1 following notes in photo 2
Alternating Series Test (AST) If {an} is and nose an = 0, lim 2x. 90 = 1/1/n >0 a decreasing seq. of positive numbers then (-1) an Conv. 9₁-92 +93-94+---- of Assume {an} is a dec. lim an = 0. Show d Show (-1) an +1 818 Let {sn} be the seq. of partial Sum of Seg of pos. # cohere Conv- the Series k
Transcribed Image Text:Alternating Series Test (AST) If {an} is and nose an = 0, lim 2x. 90 = 1/1/n >0 a decreasing seq. of positive numbers then (-1) an Conv. 9₁-92 +93-94+---- of Assume {an} is a dec. lim an = 0. Show d Show (-1) an +1 818 Let {sn} be the seq. of partial Sum of Seg of pos. # cohere Conv- the Series k
converges absolutely, converges conditionally, or diverges. 3. Find an alternating series which converges but such that the Alternat- ing Series Test does not apply. Prove that if 8 converges absolutely, then a converges 4
Transcribed Image Text:converges absolutely, converges conditionally, or diverges. 3. Find an alternating series which converges but such that the Alternat- ing Series Test does not apply. Prove that if 8 converges absolutely, then a converges 4
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