Why does the chance of "going dry" aka 0 successes in N trials with 1/N success probability approach 0.367861 as N approaches infinity? As illustrated in this R code, the chance of 0 successes in N trials with 1/N success probability seems to approach .367861, why is this? I tried to calculate it by taking the limit of the binomial cumulative density function with k=0, p=1/N, as N approaches infinity, but I couldn't get that to equal .367861, thanks.