# Tagged Questions

For questions about the evaluation of finite products, or their properties. For infinite ones, use "infinite-products" tag.

8k views

### Is $0! = 1$ because there is only one way to do nothing?

The proof for $0!=1$ was already asked at here. My question, yet, is a bit apart from the original question. I'm asking whether actually $0!=1$ is true because there is only one way to do nothing or ...
4k views

### Does multiplying all a number's roots together give a product of infinity?

This is a recreational mathematics question that I thought up, and I can't see if the answer has been addressed either. Take a positive, real number greater than 1, and multiply all its roots ...
2k views

832 views

324 views

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

How can the following integral be calculated: $$I_n=\int_0^1\int_0^1\cdots\int_0^1\frac{\prod_{k=1}^{n}\left(\frac{1-x_k}{1+x_k}\right)}{1-\prod_{k=1}^{n}x_k}dx_1\cdots dx_{n-1}dx_n$$ There should ...
561 views

309 views

### How to find the the product $\left(1 - \frac{1}{a}\right)\left(1-\frac{1}{a^{2}}\right)\left(1-\frac{1}{a^{3}}\right)\ldots$ [duplicate]
Possible Duplicate: Result of the product $0.9 \times 0.99 \times 0.999 \times \dots$ How to find the product \left(1 - \frac{1}{a}\right)\left(1-\frac{1}{a^{2}}\right)\left(1-\frac{1}{a^{3}}...
### What does $\prod_{n\geq2}\frac{n^4-1}{n^4+1}$ converge to?
What does $\prod_{n\geq2}\frac{n^4-1}{n^4+1}$ converge to? As far as I can tell, this has no closed-form solution (not saying much, I don't know much math), but a friend of mine swears he saw a ...