Decide whether each of the following statements is true or false. If a statement is true, 8 8 explain why. If a statement is false, provide specific examples of Σak and bk for k=1 which the statement is false. 8 (a) If Σ ak is a series such that k=1 ≤ak for all k, then ak diverges. k2 (c) Ifak is a series such that k < for all k, then k=1 8 if (d) If ak
Decide whether each of the following statements is true or false. If a statement is true, 8 8 explain why. If a statement is false, provide specific examples of Σak and bk for k=1 which the statement is false. 8 (a) If Σ ak is a series such that k=1 ≤ak for all k, then ak diverges. k2 (c) Ifak is a series such that k < for all k, then k=1 8 if (d) If ak
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:sum Sn.
(b) Use (a) to determine whether the series is convergent or divergent.
8
(5) Decide whether each of the following statements is true or false. If a statement is true,
explain why. If a statement is false, provide specific examples of ak and Σb for
k=1
which the statement is false.
Σ
(a) If 5 am is a series such that
ak a
k=1
1
k²
< ak for all k, then
(d) If ak
k=1
(b) If ak is a series such that 0 < a <for all k, then a converges.
Σ
k=1
if.
< b for all k = 1, 2, 3, ... and
k=1
k=1
ak diverges.
(c) Ifak is a series such that k < for all k, then a diverges.
k=1
k=1
k=1
be converges, then a converges.
bk
k=1
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