query: How can I find the limit of the following sequence $\frac{1}{2} . \frac {3}{4} ....... \frac {2n - 1}{2n} $?
positive_passages.docid: 157833
positive_passages.text: Limit of the Product $\prod_{k=1}^n\left(\frac{2k-1}{2k}\right)$
negative_passages.docid: 46830
negative_passages.text: Prove that the sequence $a_{n+1} =\frac{1}{2}\left(a_{n}+\frac{c}{a_{n}}\right)$ is convergent and find its limit
negative_passages.docid: 35169
negative_passages.text: Finding the limit of $\left(\frac{n}{n+1}\right)^n$
negative_passages.docid: 81052
negative_passages.text: Determining a limit of parametrized, recursively defined sequence $a_{n+1}=1+\frac{(a_n-1)^2}{17}$
negative_passages.docid: 4024
negative_passages.text: Finding the limit of $\frac {n}{\sqrt[n]{n!}}$
negative_passages.docid: 93095
negative_passages.text: Find $\lim\limits_{n \to \infty}\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\cdots\left(1-\frac{1}{n^2}\right)$
negative_passages.docid: 51231
negative_passages.text: Find the limit of $\frac{n^{x}}{(1 + x)^{n}}$
negative_passages.docid: 97571
negative_passages.text: Find the limit $ \lim_{n\to \infty} 2^{\frac{1}{n}}$
negative_passages.docid: 12914
negative_passages.text: What's the limit of the sequence $\lim\limits_{n \to\infty} \frac{n!}{n^n}$?
negative_passages.docid: 88782
negative_passages.text: Finding the limit of $x_1=0 , x_{n+1}=\frac{1}{1+x_n}$
negative_passages.docid: 129987
negative_passages.text: Find $\lim\frac{1}{\sqrt{n}}\left(\frac{1}{\sqrt{1}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+\ldots+\frac{1}{\sqrt{2n-1}+\sqrt{2n+1}}\right)$
negative_passages.docid: 117911
negative_passages.text: What's the limit of $\prod_1^\infty \left(1-\frac{1}{2^n}\right)=(1-1/2)(1-1/4)(1-1/8)...$?
negative_passages.docid: 99975
negative_passages.text: Find the Limit (n to infinity)
negative_passages.docid: 19100
negative_passages.text: Find $\lim \limits_{n \to \infty}{1*4*7*\dots(3n+1) \over 2*5*8* \dots (3n+2)}$
negative_passages.docid: 106707
negative_passages.text: How to find the limit of series? (What should I know?)
negative_passages.docid: 139327
negative_passages.text: Find the limit of a series of fractions starting with $\frac{1}{2}, \, \frac{1/2}{3/4}, \, \frac{\frac{1}{2}/\frac{3}{4}}{\frac{5}{6}/\frac{7}{8}}$
negative_passages.docid: 8773
negative_passages.text: Finding $\lim\limits_{n \to \infty}{\frac{1^1+2^2+3^3+\cdots+n^n}{n^n}}$