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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
2 years, 2 months ago

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Comment deleted Aug 26, 2016

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

Samuel Jones - 1 year, 1 month 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.

Samuel Jones - 2 years, 1 month ago

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

Satyajit Mohanty - 2 years, 1 month ago

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

Samuel Jones - 2 years, 1 month ago

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

Samuel Jones - 2 years, 1 month ago

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

Satyajit Mohanty - 2 years, 1 month ago

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