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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
1 year, 9 months ago

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@Satyajit Mohanty What has this link you posted got to do with the inequality? Samuel Jones · 9 months 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 · 1 year, 8 months ago

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@Satyajit Mohanty And can you please also tell what method did you use for this inequality problem or at least give a hint? Samuel Jones · 1 year, 8 months ago

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@Satyajit Mohanty @Satyajit Mohanty Sorry to disturb you again, but can you please add a solution to your 300 followers problem? Samuel Jones · 1 year, 8 months 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 · 1 year, 8 months ago

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