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**1. The problem statement, all variables and given/known data**

prove 2^n > n by induction

**2. Relevant equations**

**3. The attempt at a solution**

In my math class we start off assuming 2^n > n is true for n=k.

Then we try to prove that when n=k+1 the inequality is true. So,I

start off going, 2^(k+1) > (k+1) which is equivalent to 2*2^k > (k+1)

which is then equivalent to 2^k+2^k > (k+1) then my math teacher said

to make the next step which is, since we assumed that 2^k > k then 2^k

+ 2^k > k+k and then he said that k+k > (k+1) and that was the end of

the proof. I do not get this last part at all, since I thought that

when you prove something by induction, it's going to be proven for all

numbers but we only proved that the inequality is true for k>1