\[\Large{ e < \left( \dfrac{(n+1)^{2n+1}}{(n!)^2} \right)^\frac{1}{2n} < e^\alpha }\]

Let \(n\) be a positive integer. If \(\alpha = 1 + \dfrac{1}{12(n+1)}\), prove that the above expression holds.

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:

TopNewestComment deleted Aug 26, 2016

Log in to reply

What has this link you posted got to do with the inequality?

Log in to reply

@Satyajit Mohanty What method did you use to solve this question? Also, one of your questions has totally stumped me. Does it have a nice closed form, or do we have to evaluate it numerically? Can you post a solution to that question too? Thanks.

Log in to reply

@Samuel Jones I'll add the solution to the problem: 300 Followers Problem - Polynomial Differential Reciprocal Summations!

Log in to reply

And can you please also tell what method did you use for this inequality problem or at least give a hint?

Log in to reply

@Satyajit Mohanty Sorry to disturb you again, but can you please add a solution to your 300 followers problem?

Log in to reply

@Samuel Jones - I've added the solution to the problem 300 Followers Problem - Polynomial Differential Reciprocal Summations!. Please check it.

Log in to reply