2 votes

Which one grows faster, an exponential function where the exponent grows faster than logarithmic or a factorial powered by n?

With some manipulations: $$ f(n) = 4^{n^2 \log n} = (2^2)^{n^2 \log n} = (2^{\log n})^{2n^2} = n^{2 n^2}. $$ and: $$ g(n)= (n!)^n \le (n^n)^n = n^{n^2}. $$ Taking the limit: $$ \lim_{n \to \infty} \...
Steven's user avatar
  • 27.4k

Only top scored, non community-wiki answers of a minimum length are eligible