Prove that [tex]2n + 1 \leq 2n[/tex] for [tex]n \geq 3[/tex].

In order for something to be proven, there can be no counterexamples to prove it false.
4 ≥ 3 n = 4 2 ( 4 ) + 1 ≤ 2 ( 4 ) 8 + 1 ≤ 8 9 ≤ 8
9 is not greater than or equal to 8, therefore this statement is false .

Answered by iloveonedirection | 2024-06-10

The statement 2 n + 1 ≤ 2 n for n ≥ 3 is false. By rearranging the inequality, we find that it simplifies to 1 ≤ 0 , which is never true. Testing values like n = 3 , 4 , and 5 confirms that the inequality does not hold for these cases.
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Answered by iloveonedirection | 2025-02-23