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3. Prove that 3kN, Vn N, [n>k][1000m² + 10 ≤ n²]. Hints: you can divide both sides by n² and preserve the inequality, since n2 is always positive. Re- minder: n/nn-b. You can then figure out (in your rough work) what value of k you need. Note that 10/n2 <1 if n ≥ 4. Justify every step.

3. Prove that 3kN, Vn N, [n>k][1000m² + 10 ≤ n²]. Hints: you can divide both sides by n² and preserve the inequality, since n2 is always positive. Re- minder: n/nn-b. You can then figure out (in your rough work) what value of k you need. Note that 10/n2 <1 if n ≥ 4. Justify every step.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.6: Inequalities
Problem 77E
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4. Let R+ be the set of positive real numbers and N+ be the set of positive natural numbers. Prove that Va € R+, Vb € R+, Vp₁ € N+, Vp2 € N+, [P1 ≤ p2] ⇒ an³¹ € 0 (bn³².) You may not use, without proof, any properties of big-Oh, other than its definition. Justify every step.
Transcribed Image Text:4. Let R+ be the set of positive real numbers and N+ be the set of positive natural numbers. Prove that Va € R+, Vb € R+, Vp₁ € N+, Vp2 € N+, [P1 ≤ p2] ⇒ an³¹ € 0 (bn³².) You may not use, without proof, any properties of big-Oh, other than its definition. Justify every step.
3. Prove that k = N, Vn Є N, [n>k][1000m² + 10 ≤ n²]. Hints: you can divide both sides by n² and preserve the inequality, since n² is always positive. Re- minder: n/nn-b. You can then figure out (in your rough work) what value of k you need. Note that 10/n2 <1 if n ≥ 4. Justify every step.
Transcribed Image Text:3. Prove that k = N, Vn Є N, [n>k][1000m² + 10 ≤ n²]. Hints: you can divide both sides by n² and preserve the inequality, since n² is always positive. Re- minder: n/nn-b. You can then figure out (in your rough work) what value of k you need. Note that 10/n2 <1 if n ≥ 4. Justify every step.
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