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(c) If the series n=1 an is convergent, then n=1 Final Answer This claim is TRUE 1 sin(an+2) is convergent. n² FALSE.

(c) If the series n=1 an is convergent, then n=1 Final Answer This claim is TRUE 1 sin(an+2) is convergent. n² FALSE.

Advanced Engineering Mathematics
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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∞ 1. Let an be a POSITIVE infinite series (i.e. an > 0 for all n ≥ 1). Let ƒ 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.
Transcribed Image Text:∞ 1. Let an be a POSITIVE infinite series (i.e. an > 0 for all n ≥ 1). Let ƒ 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.
(c) If the series ∞ n=1 ∞ an is convergent, then sin(an + 2) is convergent. n² n=1 Final Answer This claim is TRUE FALSE.
Transcribed Image Text:(c) If the series ∞ n=1 ∞ an is convergent, then sin(an + 2) is convergent. n² n=1 Final Answer This claim is TRUE FALSE.
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