Prove by induction that n

Solution

If n <= 2^n

Let n = 1. Then:

              n<=2^1

              n<=2

Let n=2 Then:

       n<=2^2

              n<=4

Let n=k

           n<=2^k

          it is true for(any positive integer) k.   

   and n=k+1:

             n<=2^k+1

            this is also true (if k=any positive integer )

Hence by induction we proved that n <= 2^n for n = 1,2,3,...