most recent 30 from http://mathoverflow.net 2013-05-24T05:30:42Z http://mathoverflow.net/feeds/user/19693 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/82491/a-limit-from-an-erdos-paper Bob 2011-12-02T17:37:19Z 2011-12-03T00:33:33Z

<p>Hi,</p> <p>I need help to prove that, for $ N = \big\lfloor \frac{1}{2}n\log(n)+cn \big\rfloor $ with $c \in \mathbb R $ and $0 \leq k \leq n: $ </p> <p>$$ \lim_{n\rightarrow +\infty} \dbinom{n}{k} \frac{\dbinom{\binom{n - k}{2}}{N} }{\dbinom{\binom{n}{2} }{N}} = \frac{e^{-2kc}}{k!} $$</p>