Stirling Limit Product n^n Powers

2175ExpertCalculusSeries

Harvard-MIT Mathematics Tournament

Evaluate the limit $$ \lim_{n \rightarrow \infty} n^{-\frac{1}{2}\left(1+\frac{1}{n}\right)}\left(1^{1} \cdot 2^{2} \cdots n^{n}\right)^{\frac{1}{n^{2}}}. $$

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Stirling Limit Product n^n Powers

2175ExpertCalculusSeries

Harvard-MIT Mathematics Tournament

Evaluate the limit $$ \lim_{n \rightarrow \infty} n^{-\frac{1}{2}\left(1+\frac{1}{n}\right)}\left(1^{1} \cdot 2^{2} \cdots n^{n}\right)^{\frac{1}{n^{2}}}. $$

0 students attempted0% solvedRating 2175