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Let g: NQ be a function defined by 2n³ + 6n² + 4n 3 3 (a) Factor the numerator completely. (b) Explain, why given three consecuetive integers a, a +1, a + 2, one of them must be divisible by 3. (c) Prove that g(n) ≤ N for all natural n. (d) Is the image of g equal to N? Justify your claim. g(n) : =

Let g: NQ be a function defined by 2n³ + 6n² + 4n 3 3 (a) Factor the numerator completely. (b) Explain, why given three consecuetive integers a, a +1, a + 2, one of them must be divisible by 3. (c) Prove that g(n) ≤ N for all natural n. (d) Is the image of g equal to N? Justify your claim. g(n) : =

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 g: NQ be a function defined by 2n³ + 6n² + 4n 3 3 (a) Factor the numerator completely. (b) Explain, why given three consecuetive integers a, a +1, a +2, one of them must be divisible by 3. (c) Prove that g(n) ≤ N for all natural n. (d) Is the image of g equal to N? Justify your claim. g(n) : =
Transcribed Image Text:Let g: NQ be a function defined by 2n³ + 6n² + 4n 3 3 (a) Factor the numerator completely. (b) Explain, why given three consecuetive integers a, a +1, a +2, one of them must be divisible by 3. (c) Prove that g(n) ≤ N for all natural n. (d) Is the image of g equal to N? Justify your claim. g(n) : =
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