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} \...
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