8 1. Let an be a POSITIVE infinite series (i.e. an> 0 for all n ≥ 1). Let f be a continuous function n=1 with domain R. Is each of these statements true or false? If it is true, prove it. If it is false, prove it by providing a counterexample and justify that is satisfies the required conditions. Show Transcribed Text 3 8 Σn (3 In n=1 (e) If the series Σ an is convergent, then Σ n=1 Final Answer This claim is TRUE c 3+ an 3+an+1, FALSE. is convergent.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1. Let an be a POSITIVE infinite series (i.e. an> 0 for all n ≥ 1). Let f be a continuous function
n=1
with domain R.
Is each of these statements true or false? If it is true, prove it. If it is false, prove it by providing a
counterexample and justify that is satisfies the required conditions.
Show Transcribed Text
(e) If the series an is convergent, then ΣIn
n=1
n=1
Final Answer This claim is TRUE
3+ an
3+an+1
FALSE.
is convergent.
Transcribed Image Text:1. Let an be a POSITIVE infinite series (i.e. an> 0 for all n ≥ 1). Let f be a continuous function n=1 with domain R. Is each of these statements true or false? If it is true, prove it. If it is false, prove it by providing a counterexample and justify that is satisfies the required conditions. Show Transcribed Text (e) If the series an is convergent, then ΣIn n=1 n=1 Final Answer This claim is TRUE 3+ an 3+an+1 FALSE. is convergent.
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