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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 4. If the series Σan is divergent, then Σ-11 n=1 anis 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 4. If the series Σan is divergent, then Σ-11 n=1 anis divergent.

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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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
Transcribed Image Text: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
4. If the series Σan is divergent, then Σ-11 n=1 anis divergent.
Transcribed Image Text:4. If the series Σan is divergent, then Σ-11 n=1 anis divergent.
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