query: $a_0 = 5/2$. $a_k = (a_{k-1})^{2} - 2$ for $k\geq1. \prod_{k=0}^{\infty}{\left(1-1/a_k\right)}.$
positive_passages.docid: 24924
positive_passages.text: Computing an infinite product
negative_passages.docid: 157833
negative_passages.text: Limit of the Product $\prod_{k=1}^n\left(\frac{2k-1}{2k}\right)$
negative_passages.docid: 63672
negative_passages.text: Understanding a particular evaluation of $\prod\limits_{n=2}^{\infty}\left(1-\frac{1}{n^3}\right)$
negative_passages.docid: 51679
negative_passages.text: Simplifying the product $\prod\limits_{k=2}^n \left(1-\frac1{k^2}\right)$
negative_passages.docid: 23919
negative_passages.text: Trying to evaluate $\prod_{k=1}^{n-1}(1-e^{2k\pi i/n})$ for my complex analysis homework
negative_passages.docid: 21921
negative_passages.text: Showing that $|f(z)| \leq \prod \limits_{k=1}^n \left|\frac{z-z_k}{1-\overline{z_k}z} \right|$
negative_passages.docid: 60061
negative_passages.text: Find the value of : $\lim_{n\to\infty}\prod_{k=1}^n\cos\left(\frac{ka}{n\sqrt{n}}\right)$
negative_passages.docid: 85882
negative_passages.text: Show that $1\otimes (1,1,\ldots)\neq 0$ in $\mathbb{Q} \otimes_{\mathbb{Z}} \prod_{n=2}^{\infty} (\mathbb{Z}/n \mathbb{Z})$.
negative_passages.docid: 13390
negative_passages.text: Recursive Monotone Decreasing Sequence Proof ${x_{k}} = \frac{1}{2}\left({x_{k-1}+\frac{a}{{x_{k-1}}}}\right)$
negative_passages.docid: 88130
negative_passages.text: Infinite product $\prod_k (1-z/a_k)(1-z/b_k)^{-1}$ converges uniformly on compacts of$\{\mathbb Im z>0\}$ and is Herglotz
negative_passages.docid: 7843
negative_passages.text: Show that order of $a^k$
negative_passages.docid: 30356
negative_passages.text: $a =\prod_{i = 1}^{r} p_{i}^{ai}$ with $a_{i} > 0$ for each $i$ is the canonical representation of $a$...
negative_passages.docid: 146221
negative_passages.text: Find the product $\prod_{n=1}^{\infty} (1+x^{2n-1}) $
negative_passages.docid: 40784
negative_passages.text: $\sum_{k=m}^{n}(-1)^k\binom{n}{k}\binom{k}{m}=0, n>m\geq 0$
negative_passages.docid: 126574
negative_passages.text: Proving $\prod_k \sin \pi k / n = n / 2^{n-1}$
negative_passages.docid: 64501
negative_passages.text: Homework: limit of $\frac{1}{n}\sqrt[n]{\prod_{k=1}^n(n+k)}$ as $n\to\infty$
negative_passages.docid: 281
negative_passages.text: How one can prove $\prod_{k=1}^{n-1} (\cos\theta-\cos(k\pi/n)) = 2^{1-n}\sin(n\theta)\csc\theta$?