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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.

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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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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