Newbetuts

How to show that $ \left(1+\frac{1}{n} \right)^n = \sum_{i=0}^{n}\frac{1}{i!}\left(\prod_{j=0}^{i-1}\left(1 - \frac{j}{n}\right)\right)$ [duplicate]

Calculate $(i+u_0)(i+u_1)\cdots(i+u_{n-1})$ if $u_0,u_1,...u_{n-1}$ are $n-$th roots of unity [closed]

How to compute the following integral in $n$ variables?

What is a good upper bound $n^n(n-1)^{n-1}\ldots2^21^1$?

Prove that a set of nine consecutive integers cannot be partitioned into two subsets with same product

Does a brand name used as common noun like Hoover respond to change in market share made by Dyson? [closed]

proof of $\sum\nolimits_{i = 1}^{n } {\prod\nolimits_{\substack{j = 1\\j \ne i}}^{n } {\frac{{x_i }}{{x_i - x_j }}} } = 1$ [duplicate]

Can the limit of a product exist if neither of its factors exist?

Product Identity Multiple Angle or $\sin(nx)=2^{n-1}\prod_{k=0}^{n-1}\sin\left(\frac{k\pi}n+x\right)$ [duplicate]

Proof of $\sin nx=2^{n-1}\prod_{k=0}^{n-1} \sin\left( x + \frac{k\pi}{n} \right)$

Evaluation of $\prod_{n=1}^\infty e\left(\frac{n}{n+1}\right)^{n}\sqrt{\frac{n}{n+1}}$

If a product exists for a set of objects in a category, then is there a product in the category for every subset of those objects?

What is $\mathcal{R}$?

Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.

What does $\prod_{i<j} (j - i)$ mean where $i,j\in\{1,2,\ldots,8\}$?

Is there a "continuous product"?

Simplify $\prod_{k=1}^5\tan\frac{k\pi}{11}$ and $\sum_{k=1}^5\tan^2\frac{k\pi}{11}$

New posts in products

How to show that $ \left(1+\frac{1}{n} \right)^n = \sum_{i=0}^{n}\frac{1}{i!}\left(\prod_{j=0}^{i-1}\left(1 - \frac{j}{n}\right)\right)$ [duplicate]

A question about $\prod_{x\in \mathbb{R}^{*}}{x}$

Why is empty product defined to be $1$? [duplicate]

Prove that the product of some numbers between perfect squares is $2k^2$ [duplicate]

Calculate $(i+u_0)(i+u_1)\cdots(i+u_{n-1})$ if $u_0,u_1,...u_{n-1}$ are $n-$th roots of unity [closed]

How to compute the following integral in $n$ variables?

What is a good upper bound $n^n(n-1)^{n-1}\ldots2^21^1$?

Prove that a set of nine consecutive integers cannot be partitioned into two subsets with same product

Does a brand name used as common noun like Hoover respond to change in market share made by Dyson? [closed]

proof of $\sum\nolimits_{i = 1}^{n } {\prod\nolimits_{\substack{j = 1\\j \ne i}}^{n } {\frac{{x_i }}{{x_i - x_j }}} } = 1$ [duplicate]

Can the limit of a product exist if neither of its factors exist?

Product Identity Multiple Angle or $\sin(nx)=2^{n-1}\prod_{k=0}^{n-1}\sin\left(\frac{k\pi}n+x\right)$ [duplicate]

Proof of $\sin nx=2^{n-1}\prod_{k=0}^{n-1} \sin\left( x + \frac{k\pi}{n} \right)$

Evaluation of $\prod_{n=1}^\infty e\left(\frac{n}{n+1}\right)^{n}\sqrt{\frac{n}{n+1}}$

If a product exists for a set of objects in a category, then is there a product in the category for every subset of those objects?

What is $\mathcal{R}$?

Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.

What does $\prod_{i<j} (j - i)$ mean where $i,j\in\{1,2,\ldots,8\}$?

Is there a "continuous product"?

Simplify $\prod_{k=1}^5\tan\frac{k\pi}{11}$ and $\sum_{k=1}^5\tan^2\frac{k\pi}{11}$