4. Determine whether the following statements are true and give an explanation or counterexample. -k a) Ex=1 (²) is a convergent geometric series. b) If a is a real number and 12 a ak converges, then Σ-1 ak converges. 00 c) If the series -₁ ak converges and |a| < |b|, then the series Σ₁bk converges. 00
4. Determine whether the following statements are true and give an explanation or counterexample. -k a) Ex=1 (²) is a convergent geometric series. b) If a is a real number and 12 a ak converges, then Σ-1 ak converges. 00 c) If the series -₁ ak converges and |a| < |b|, then the series Σ₁bk converges. 00
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:4. Determine whether the following statements are true and give an explanation or
counterexample.
-k
a) _E=1(3)
() is a convergent geometric series.
b) If a is a real number and Σ-12 ak converges, then Σ=₁ ak converges.
100
c) If the series -1 ak converges and la| < |b|, then the series -
bk
=1
converges.
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