mathematical induction

Question

Show that for all integers greater than zero : 2n >= n+1.

Answer 1

Suppose that the statement is true for n, i.e., 2n >= n+1 (inductive assumption)

Then, for n+1, one finds using the inductive assumption, that

 

2(n+1) = 2n+2 >= (n+1)+2 > (n+1)+1.

 

Since the statement obviously holds for n=1 (2*1=1+1) and n=2 (2*2> 2+1), you are done!