# Help! What series get larger value when n is sufficiently large

1. Nov 20, 2009

### esvee

1. The problem statement, all variables and given/known data

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)

2. Nov 20, 2009

### jgens

3. Nov 20, 2009

### Office_Shredder

Staff Emeritus
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

4. Nov 20, 2009

### jgens

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

5. Nov 21, 2009

### esvee

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*

6. Nov 21, 2009

### Count Iblis

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).