I wonder if someone could clarify these limits for me. They arise in the derivation of the poisson distribution from the binomial distribution as

and

The first is

as

.

I don't see how this works. If anything I would have thought that

as

.

The second is that

\frac{n!}{(n-k)!(n-\lambda)^k = \frac{n(n-1) \ldots (n-k+1)}{(n - \lambda) (n-\lambda) \ldots (n - \lambda)}

is a "quantity that tends to 1 as

(since

remains constant)."

What precisely is the role of

? Is the critical condition not that the numerator and denominator grow at the same rate, and if so, how can this be demonstrated?

Thanks in advance. MD