\[\displaystyle \lim_{n \to \infty} {\left(\dfrac{\displaystyle \prod_{\substack{m \left \lfloor n/t\right \rfloor \le k \le mn \\ k\mod{m} \equiv p}} k}{\displaystyle \prod_{\substack{m \left \lfloor n/t\right \rfloor \le k \le mn \\ k\mod{m} \equiv q}} k }\right)} = t^{(p-q)/m}\]

Try to prove this. Observe what all it is trying to express.

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestOkay, here is the solution.

Log in to reply