what is a counterexample that disproves 3n<3^n

Question

a) n= -1

b) n=0

c) n=1

d) n=2

Answer 1

Quick and dirty way: plug it in!

 

a) 3(-1) < 3^-1

    -3 < 1/3  True

b) 3(0) < 3⁰

     0 < 1 True

c) 3(1) < 3¹

      3 < 3 FALSE

d) 3(2) < 3²

     6 < 9 True

 

Answer is C