Calculate ${2^{n + 1}}\prod\limits_{k = 1}^n {\cos \frac{{\pi k}}{{n + 1}}} $
59003
Product of cosines: $ \prod_{r=1}^{7} \cos \left(\frac{r\pi}{15}\right) $
22636
Find the sum of the series $\sum \limits_{n=1}^{\infty} \frac{2^{-n}(n+3)}{(n+1)(n+2)}$
141404
Infinite product: $\prod_{k=2}^{n}\frac{k^3-1}{k^3+1}$
37484
Is there an elementary argument to show that $\prod_{n=0}^\infty \frac{2n+1}{2n+3}=0$
56365
Evaluate $\sum\limits_{k=1}^{n} \frac{k}{2^k}$
105697
How do I evaluate $\prod_{r=1}^{\infty }\left (1-\frac{1}{\sqrt {r+1}}\right)$?
4578
Evaluate the value of $\lim_{n \to \infty}\frac{x_n}{\prod_{i=1}^{n-1} x_i}$ where $x_n=x_{n-1}^2-2, x_1=5$
64501
Homework: limit of $\frac{1}{n}\sqrt[n]{\prod_{k=1}^n(n+k)}$ as $n\to\infty$
114418
A deduction from $x^n-1=(x^2-1)\prod_{k=1}^{(n-2)/2}[x^2-2x\cos{\frac{2k\pi}{n}}+1]$
60290
Calculate $\lim_{n\to\infty}\left(\prod_{i=3}^n\sec\frac{\pi}{i}\right)$
64581
How to find the sum $\sum\limits_{k=1}^n (k^2+k+1)k!$?
103843
Infinite Series $\sum\limits_{n=1}^{\infty}\frac{1}{\prod\limits_{k=1}^{m}(n+k)}$
5054
Calculate $\sum\limits_{k=0}^{\infty}\frac{1}{{2k \choose k}}$
78033
Evaluating $\prod_{n=1}^{\infty}\left(1+\frac{1}{2^n}\right)$
13864
$\prod_{k=0}^{\infty} \cos(x \cdot 2^{-k}).$
13796
What is the value of $\prod_{n=1}^\infty (1+\frac{1}{n^2})$?
116019
Find the limit $\lim\limits_{n\to \infty}\sum\limits_{k=1}^{n}\left(\frac{k}{n^2}\right)^{\frac{k}{n^2}+1}$