3. Prove thatk = 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. Notethat 10/n2 <1 if n ≥ 4. Justify every step.

Answer 3 Given, a statement: It is required to prove the existence of a natural number such that…

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.