An ugly looking limit

Calculus Level 2

Find lim ⁡ n → ∞ atan ⁡ ( n ! + 2 2 n n n ) n \lim\limits_{n \to \infty} \frac{\operatorname{atan} \left ( n! + \frac{2^{2^n}}{n^n}\right )}{n}


The answer is 0.

Тимофей Ломоносов by Тимофей Ломоносов , 28, Russia

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1 solution

Otto Bretscher
Dec 1, 2015

The given expression is positive and less than π 2 n \frac{\pi}{2n} , so that the limit is 0 \boxed{0} by the squeeze theorem.

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