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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
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.
Expert Solution
steps

Step by step

Solved in 3 steps with 30 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,