1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
Hello, I am working on the problem in the attached image regarding induction based on the inequality
[tex]2^n \geq n + 1[/tex]
I am confused how to do this by proving that if it is assumed to be true for [tex]k[/tex], then how it is true for [tex]k + 1[/tex]. The way I see it, you would just do [tex] 2^{k+1} \geq (k+1) + 1[/tex]. The answer is [tex] 2(k+1) \geq k + 2[/tex], but I do not understand it.
EDIT: by the way, how do I get this latex to not start a new line??
2. Relevant equations
3. The attempt at a solution
Hello, I am working on the problem in the attached image regarding induction based on the inequality
[tex]2^n \geq n + 1[/tex]
I am confused how to do this by proving that if it is assumed to be true for [tex]k[/tex], then how it is true for [tex]k + 1[/tex]. The way I see it, you would just do [tex] 2^{k+1} \geq (k+1) + 1[/tex]. The answer is [tex] 2(k+1) \geq k + 2[/tex], but I do not understand it.
EDIT: by the way, how do I get this latex to not start a new line??
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