How to solve: $\ \lim_{n \to +\infty} \frac{n^n + \frac {1}{n}}{(n + \frac {1}{n})^n} \ t^n $

Question

How can I solve:

$$\ \lim_{n \to +\infty} \frac{n^n + \frac {1}{n}}{(n + \frac {1}{n})^n} \ t^n $$

tis a whole number.

Thank you very much! Please tell me your ideas, even if you won't post the the result.

Answer 1

This is basically just a guess, but I would expect the limit to be $\infty$. Since $n \to \infty$, $\frac 1 n \to 0$, so we can ignore that term, giving us: $$\lim_{n \to \infty} \frac{n^n}{n^n} t^n=\lim_{n \to \infty} t^n=\infty$$