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Math Induction problem

  • Thread starter skeough15
  • Start date
  • #1
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Homework Statement


We are asked to try and prove the values n where n2 < 2(n) .
It asks us to prove it by Math Induction.

The Attempt at a Solution


I can see it works for n=0 and n=1 but not for n=2,3,4 . So I made my base step n=5 and showed that 52 = 25 < 25 =32 as 25<32. I then started simple mathematical induction off by assuming that n2<2n for n>5, and tried to prove it using (n+1)2<2(n+1) but can't seem to get that proven. Any suggested help on how to prove that?
 
Last edited:

Answers and Replies

  • #2
22,097
3,278


It seems that you need to show that [tex]2n+1<2^n[/tex]... Maybe another induction?
 
  • #3
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yes that is exactly what I had to do, I assume it is sufficient to have an induction proof within an induction proof?
 
  • #4
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3,278


I cant really see a problem with that...
 

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