3. Prove that 3 € N, \n € N, [n > k] ⇒ [1000m² + 10 ≤ n³]. Hints: you can divide both sides by n² and preserve the inequality, since n² is always positive. Re- minder: nº/n=n-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 3 € N, \n € N, [n > k] ⇒ [1000m² + 10 ≤ n³]. Hints: you can divide both sides by n² and preserve the inequality, since n² is always positive. Re- minder: nº/n=n-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
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 67E
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