Let Σan be a POSITIVE infinite series (i.e. an > 0 for all n ≥ 1 ). Let ƒ be a continuous function 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. 1. If ±1 (an+an+1) is convergent, then Σ ª is convergent. 2n=1 2. If the series Σn=1 an is convergent, then Σ arctan (1+an) is divergent.

Let Σan be a POSITIVE infinite series (i.e. an > 0 for all n ≥ 1 ). Let ƒ be a continuous function 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. 1. If ±1 (an+an+1) is convergent, then Σ ª is convergent. 2n=1 2. If the series Σn=1 an is convergent, then Σ arctan (1+an) is divergent.

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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