(a) Give an example of a series Σ an where an <✓ for n ≥ 2 and Σan converges. n=2 n=2 (b) Give an example of a series Σ an where an < ✓ for n ≥ 2 and Σ an diverges. n=2 √n n=2 Note: These two examples show why in Direct Comparison Test if an

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 30E
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(a) Give an example of a series Σ an where an <✓ for n ≥ 2 and Σan converges.
n=2
n=2
(b) Give an example of a series Σ an where an < ✓ for n ≥ 2 and Σ an diverges.
n=2
√n
n=2
Note: These two examples show why in Direct Comparison Test if an <bn and bn diverges
we get NO INFORMATION
Transcribed Image Text:(a) Give an example of a series Σ an where an <✓ for n ≥ 2 and Σan converges. n=2 n=2 (b) Give an example of a series Σ an where an < ✓ for n ≥ 2 and Σ an diverges. n=2 √n n=2 Note: These two examples show why in Direct Comparison Test if an <bn and bn diverges we get NO INFORMATION
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