I was wondering how fast x! grows as it approaches infinity as compared to x(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}, 2^{x}, and x^{x}. The last one was fairly obvious since x*x*x*x... > x(x-1)(x-2)(x-3)... But I can't figure out a way to show that x! grows faster than x^{2}or 2^{x}. I know it grows faster since I can compare the graphs of the functions on my calculator but I want to understand why. This since it seems like it would be helpful in solving limits where x approaches infinity, and using the comparison test for series which involve factorials.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Rate of growth of factorials.

**Physics Forums | Science Articles, Homework Help, Discussion**