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∞ ∞ o) If the series an is convergent, then arctan(1 + an) is divergent. n=1 n=1 Final Answer This claim is TRUE FALSE.

∞ ∞ o) If the series an is convergent, then arctan(1 + an) is divergent. n=1 n=1 Final Answer This claim is TRUE 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.
∞ (b) If the series an is convergent, then arctan(1 + an) is divergent. n=1 n=1 Final Answer This claim is TRUE FALSE.
Transcribed Image Text:∞ (b) If the series an is convergent, then arctan(1 + an) is divergent. n=1 n=1 Final Answer This claim is TRUE FALSE.
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