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Is $\prod_{i=1}^{n}x_{i} > \prod_{i=1}^{n}y_{i} \implies \prod_{i=1}^{n}(x_{i}+k) > \prod_{i=1}^{n}(y_{i}+k)$ true?

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Dot Product proof that results in the smallest set

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LogLiklihood Function and Fisher Information Martix

Product of edge lengths of a complete graph

How do I prove this complex-looking sum-product equation?

Help simplifying a product

Prove that $\vert\sin(x)\sin(2x)\sin(2^2x)\cdots\sin(2^nx)\vert < \left(\frac{\sqrt{3}}{2}\right)^n$

Polynomials tending to $\exp (t^2/2)$

Simplify $\prod_{i=0}^n \frac {c-i} c$

Show that the given products are equal

Evaluation of $\sum_{i=1}^n\cfrac{\beta_i^k}{\prod_{j=1\\j\neq i}^n (\beta_j-\beta_i)}$

Asymptotics of q-Pochhammer symbol

Prove or refute these lemmas that I've deduced concerning examples to the Pólya class

Limit of a sequence including infinite product. $\lim\limits_{n \to\infty}\prod_{k=1}^n \left(1+\frac{k}{n^2}\right)$

The limit of this sequence.

Is $\prod_{i=1}^{n}x_{i} > \prod_{i=1}^{n}y_{i} \implies \prod_{i=1}^{n}(x_{i}+k) > \prod_{i=1}^{n}(y_{i}+k)$ true?

Dot Product proof that results in the smallest set

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