# Inequality on $e$

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

Let $n$ be a positive integer. If $\alpha = 1 + \dfrac{1}{12(n+1)}$, prove that the above expression holds. Note by Satyajit Mohanty
5 years ago

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@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.

- 4 years, 11 months ago

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

- 4 years, 11 months ago

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

- 4 years, 11 months ago

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

- 4 years, 11 months ago