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Bounding the product of a sequence
I am trying to find an upper bound for the following sequence:
$$(1-p_1)(1-(p_1+p_2))\cdots(1-(p_1+\cdots+p_n))$$
with $n$ groups to multiply. I have written it like this:
$$\prod_{i=1}^n \left({1 ...
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Asymptotics of a Product of Rational Expressions
The following is taken from page 8 of Alon and Spencer's The Probabilistic Method.
$$ \prod_{i = 0}^{n-1} \frac{v - 2i}{v-i} \sim e^{-n^2/2v} $$ as long
as $v \gg n^{3/2}$, estimating
...
