/sci/ - Science & Math

Is this valid?

<span class="math"> (\frac {3}{n})^n = (\frac {3}{n})^n [/spoiler]

<span class="math"> (\frac {3}{n})^n = 3^n * (\frac {1}{n})^n[/spoiler]

<span class="math"> \lim_{n \to \infty} (3^n * (\frac {1}{n})^n) = (\lim_{n \to \infty} (3^n)) * (\lim_{n \to \infty} (\frac {1}{n}))^n[/spoiler]

<span class="math">\to \lim_{n \to \infty} (3^n) * (0)^n[/spoiler]

<span class="math"> = 0 [/spoiler]

I'm not sure about whether it is valid to do the third to last step.