Prove 2^n >n for all n belonging to the set of natural numbers

for n=1 2^1=2  2>1 hence true for n=1 assume true for n then 2^n >n we need to show 2^n+1 > n+1 since 2^n >n 2^n+1 >2n =n+n >n+1 for n>1 hence by induction since true for n= 1 and if true for n then true for n+1 the statement is true for all natural numbers