Simple Proof by InductionDate: 08/27/99 at 06:10:52 From: Karim Bourouba Subject: Proof by Induction Hi, Here's my question: Show by mathematical induction that the proposition below is true: If n >= 1 then 3n >= 1 + 2n -Karim Date: 08/28/99 at 02:39:17 From: Doctor Floor Subject: Re: Proof by Induction Dear Karim, Thanks for sending your question. The induction proof: 1. For n = 1 the statement is true, because then the statement reads 3 >= 3. 2. Suppose that the statement is true for m, so 3m >= 1 + 2m. We consider m+1: 3(m+1) >= 1 + 2(m+1) (3m) + 3 >= (1 + 2m) + 2 So the "3n" part grows more than the "1+2n" part, and we can conclude that: 3(m+1) >= 1 + 2(m+1). And the proof using mathematical induction stands. Best regards, - Doctor Floor, The Math Forum http://mathforum.org/dr.math/ |
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