Hi,

I'm familiar with induction with equal signs. We did it in high school. However I can't seem to understand out to prove by induction using the logical operator '<' (less than).

And i'm stuck on this question. All help is greatly appreciated.

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- Jun 18th 2010, 09:47 PMatSydneyUniprove 3^n < n! for all n>=7
Hi,

I'm familiar with induction with equal signs. We did it in high school. However I can't seem to understand out to prove by induction using the logical operator '<' (less than).

And i'm stuck on this question. All help is greatly appreciated. - Jun 18th 2010, 09:59 PMundefined
So the base case is n = 7. You need to show that

3^7 < 7!

Then consider that whenever you increase n by 1, you multiply the left side by 3, and the right side by a number greater than 3. Thus the right side will continue to be greater than the left side. This is what you will write formally as the induction step. (Assume 3^n < n!. Then show that 3^(n+1) < (n+1)! is true.) - Jun 18th 2010, 10:02 PMatSydneyUni
OHHHH....

so we have to explicitly state that the LHS grows quicker than the RHS in the inductive step...

thank you kindly, THank you very much indeed. - Jun 18th 2010, 10:45 PMundefined