Let (-1)n-1un be an alternating series. The Alternating Series Test (AST) has 3 conditions to check for convergence. They are: O (1) un can alternate. (2) un≥ Un+1. (3) lim un=0. n→∞ Ⓒ (1) un≥ 0 for all n. (2) un≥ Un+1 for n large enough. (3) _lim un=0. nco O (1) un≥ 0 for all n. (2) un≤ Un+1 for n large enough. (3) _lim un=0. n→∞ O (1) un≥ 0 for all n. (2) un≥ Un+1 for n large enough. (3) lim un*0.
Let (-1)n-1un be an alternating series. The Alternating Series Test (AST) has 3 conditions to check for convergence. They are: O (1) un can alternate. (2) un≥ Un+1. (3) lim un=0. n→∞ Ⓒ (1) un≥ 0 for all n. (2) un≥ Un+1 for n large enough. (3) _lim un=0. nco O (1) un≥ 0 for all n. (2) un≤ Un+1 for n large enough. (3) _lim un=0. n→∞ O (1) un≥ 0 for all n. (2) un≥ Un+1 for n large enough. (3) lim un*0.
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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Transcribed Image Text:Let Σ(-1)n-1un be an alternating series. The Alternating Series Test (AST) has 3 conditions to check for convergence. They are:
O (1) un can alternate. (2) un≥ Un+1. (3) lim un=0.
n→∞
lim un=0.
n→∞
O (1) un≥ 0 for all n. (2) un≥ Un+1 for n large enough. (3)
O (1) un≥ 0 for all n. (2) un≤ Unt1 for n large enough. (3) lim un=0.
n→∞
O (1) un≥ 0 for all n. (2) un≥ Un+1 for n large enough. (3) lim un‡0.
n→∞
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