$\prod_{k=0}^{\infty} \cos(x \cdot 2^{-k}).$
4644
Finding the limit $\lim \limits_{n \to \infty}\ (\cos \frac x 2 \cdot\cos \frac x 4\cdot \cos \frac x 8\cdots \cos \frac x {2^n}) $
117911
What's the limit of $\prod_1^\infty \left(1-\frac{1}{2^n}\right)=(1-1/2)(1-1/4)(1-1/8)...$?
59253
Summing the power series $\sum\limits_{n=0}^\infty (-1)^n \frac{x^{2n+1}}{2n+1}\prod\limits_{k=1}^n\frac{2k-1}{2k} $
15259
Proving $\prod \limits_{k=0}^{n}(1-a_k) \geq1- \sum\limits_{k=0}^{n}a_k$
23919
Trying to evaluate $\prod_{k=1}^{n-1}(1-e^{2k\pi i/n})$ for my complex analysis homework
63672
Understanding a particular evaluation of $\prod\limits_{n=2}^{\infty}\left(1-\frac{1}{n^3}\right)$
73375
Show that $\prod (1- P(A_n))=0$ iff $\sum P(A_n) = \infty$
104319
Real solution of $(\cos x -\sin x)\cdot \bigg(2\tan x+\frac{1}{\cos x}\bigg)+2=0.$
30356
$a =\prod_{i = 1}^{r} p_{i}^{ai}$ with $a_{i} > 0$ for each $i$ is the canonical representation of $a$...
81589
Find the sum of $\sum_{k=0}^{\infty} 1/[(r+2k+2)(s+2k+2)]$
117200
Evaluation of $ \sum_{k=0}^n \cos k\theta $
40537
How to prove $\int_0^\infty e^{-x^2}cos(2bx) dx = \frac{\sqrt{\pi}}{2} e^{-b^2}$
98933
Calculating the sum of $f(x) = \sum_{n=0}^{\infty} {n \cdot 2^n \cdot x^n}$
93085
How to prove the identity $\prod_{n=1}^{\infty} (1-q^{2n-1}) (1+q^{n}) =1 $ for $|q|<1$?
725
proof of $\sum_{n=1}^\infty n \cdot x^n= \frac{x}{(x-1)^2}$
92588
Showing that $(C_0([0,\infty)), \|\cdot\|_\infty)$ is complete.
62012
What is $0\div0\cdot0$?