Question

Use the principle of mathematical induction to prove that 1 2 n n( 1)... 2 n > × − × × for all n ∈ N. Is there any part of the proof of that uses deductive reasoning? Give reasons for your answer.

25 Apr 2023
Answer :
Word Count : 381

To prove the inequality 1 * 2 * 3 * ... * 2^n > (n+1)!/2^(n+1) for all n ∈ N using mathematical induction, we need to follow two steps:

Step 1: Base Case
We first establish that the inequality holds for the base case, which is n = 1.
When n = 1, the inequality becomes 1 * 2 > (1+1)!/2^(1+1), which simplifies to 2 > 2, which is true.

Step 2: Inductive Step
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