# Tagged Questions

74 views

### Can we get the formula for $\prod\limits_{k=0}^n{(1+2^k)^2}$ in terms of $n$?

Can we get the formula for $\prod\limits_{k=0}^n{(1+2^k)^2}$ in terms of $n$?
I am interested in the asymptotics of $$1-\prod_{i=0}^{k-1}\left(1-\frac{i}{2^k}\right).$$ As a rough piece of mostly incorrect work this looks a little like $$1-\prod_{i=0}^{k-1}e^{-i/2^k} = ... 0answers 30 views ### Simplifying products Sorry for the very general title, but I don't even know how to name my question. I got a formula which is: f(n)=\prod_{i = 0}^{\infty} ((n \; \mathrm{rem} \; p^{i + 1}) \; \mathrm{div} \; p^i + 1) ... 0answers 81 views ### Bounding the product of a sequence I am trying to find an upper bound for the following sequence:$$(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 ...
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 ...