Question

Show that 2^n>n^3 for n> 10 ​

Answer 1

Answer:

For another way just using n>9, note that when n=10, 2n=1024>1000=n3. Now suppose that 2n>n3 for n>9. Then,

2n+1=2⋅2n>2n3=n3+n3>n3+9n2=n3+3n2+6n2>n3+3n2+54n=n3+3n2+3n+51n>n3+3n2+3n+1=(n+1)3