(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that 3^n >= 2n+1 for all natural numbers.

2. Relevant equations

3^n >= 2n+1 [is bigger or equal to]

3. The attempt at a solution

3*1>=2+1

True for n=1

Assumption: 3^k>=2k+1

3^(k+1)>=2k+3

3^k*3>=2k+3

(2k+1)*3>=2k+3 <---can I just substitute 2k+1 into 3^k as per my assumption, because 3^k is bigger, and (2k+1)*3 is bigger than 2k+3? If so, is the proof complete?

Thanks in advance.

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# Homework Help: Proof by induction question

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