Prove by induction that 3^n>n^3 where n>3 please.
Originally Posted by Rubberduckzilla Prove by induction that 3^n>n^3 where n>3 please.
Verify n = 4 : sure enough, true.
Assume true for n = k - 1 :
Prove for n = k:
Left Side =
the last inequality is true because:
When k = 4, we have 1/3 < 9/16
When k = 5, we have 1/3 < 16/25
as k goes to infinity: we have (1/3) < 1