Calculating $\lim_{n \to \infty}\left(\frac{1^n +2^n +3^n + \cdots + n^n}{n^n}\right)$

Asked May 10 '16 at 14:53

Active Apr 30 '19 at 19:17

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Evaluate :

$$\lim_{n \to \infty}\left(\frac{1^n +2^n +3^n + \cdots + n^n}{n^n}\right)$$

I tried using squeeze theorem, but I couldn't find the proper inequality. I also thought of using the Stolz–Cesàro Theorem but it further complicated the problem.

Any help will be appreciated.
Thanks.

edited Jun 12 '20 at 10:38

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asked May 10 '16 at 14:53

Henry

5,549

$$\sum_{k = 0}^{n-1} \biggl( 1 - \frac{k}{n}\biggr)^n.$$ I think it has been asked before. Let me look. – Daniel Fischer May 10 '16 at 14:59

Calculating $\lim_{n \to \infty}\left(\frac{1^n +2^n +3^n + \cdots + n^n}{n^n}\right)$

0 Answers0