Recent content by koroviev

Thanks for the reply! (And sorry that I put in this wrong forum originally -- I got the problem from a computer science professor, but the problem is probably more math now that I think about it). I actually ended up solving the problem myself, though my methods probably aren't the most elegant...

Homework Statement If k is a natural number, prove that 2^{n} > n^{k} for all n \geq k^{2} + 1.Homework Equations We need to use a proof by induction.The Attempt at a Solution Let's do the case when k = 4. We check the base case directly: 2^{17} = 131072 > 83521 = 17^4 Suppose 2^{n} > n^{4} for...