Prove that 3³³ + 4³³ + 5³³ < 6³³

Replace 33 in the problem statement with "n", and examine n=1,2,3,4 etc.  Note that power functions increase monotonically.  Once n>3, the RHS of the equation is greater than the LHS.  In addition, for n>3, the difference between the RHS and LHS increases for increasing n (i.e. RHS-LHS is also increasing monotonically).  QED.

Posted by Kenny M on 2021-01-25 07:31:09