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#1 2011-10-26 05:45:08

JohnJ
Member
Registered: 2011-10-26
Posts: 2

Help with a Big Oh problem please

Hi folks,

Preparing for an exam and have to figure this one out. I have no idea where to start and any help would be most welcome. Thanks in anticipation.

a is a positive constant
n is a natural number

Show that a^n = O(n!)

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#2 2011-10-26 06:54:25

TheDude
Member
Registered: 2007-10-23
Posts: 361

Re: Help with a Big Oh problem please

By the definition of Big O notation, we want to find an M and x such that

Let's try x = a and solve for M:

We've constructed x and M such that our original inequality holds at n = a.  Use mathematical induction to prove it for n > a:


Wrap it in bacon

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