Define Exhaustive proof.Given that n is a positive

Ahnaf Ome

Ahnaf Ome

Answered question

2022-07-05

Define Exhaustive proof.Given that n is a positive integer and n ≤ 4: prove that (n + 1)3 3n.

 

Answer & Explanation

nick1337

nick1337

Expert2023-06-17Added 777 answers

To prove: (n+1)3>3n for all positive integers n satisfying n4.
Proof by exhaustive case analysis:
Case 1: n=1
(1+1)3=8>3(1)=3
Case 2: n=2
(2+1)3=27>3(2)=6
Case 3: n=3
(3+1)3=64>3(3)=9
Case 4: n=4
(4+1)3=125>3(4)=12
Since the inequality holds for all cases, we conclude that (n+1)3>3n for all positive integers n satisfying n4.

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