Help What series get larger value when n is sufficiently large

[esvee]

Homework Statement

i'm stuck on this question for a long time now, any help would be greatly appreciated..

which of the series gets larger values when n is sufficiently large:

n! or n^(10^10)

 

[jgens]

Stirling's approximation would be very helpful if you know that. If you're unfamiliar with it, there's a brief article on it here: http://en.wikipedia.org/wiki/Stirling's_approximation

 

[Office_Shredder]

You don't really need that. There is a value of n so that n/2>10¹⁰ (obviously)

Now try to bound n! from below by a polynomial for very large n

 

[jgens]

You don't really need that.

Obviously you don't, it just makes the problem considerably simpler.

 

[esvee]

You don't really need that. There is a value of n so that n/2>10¹⁰ (obviously)

Now try to bound n! from below by a polynomial for very large n

thanks for the replies!

i still don't get it, i tried various ways using the sterling approximation (i'm pretty sure I'm not allowed to use it in this coursework) and by trying to take log10 out of both of the "inequality's" sides... i can't find use for the fact that n/2 is larger than 10¹⁰.

*going crazy*

 

[Count Iblis]

Obviously you don't, it just makes the problem considerably simpler.

The problem with using Stirling is that you wouldn't have rigorously proved the statement if you don't know how to derive Stirling rigorously (including with a rigorous error term).