I've spent the better part of this day trying to show from first principles that this sequence tends to 1. Could anyone give me an idea of how I can approach this problem?
lim
Answer
You can use \text{AM} \ge \text{GM}.
\frac{1 + 1 + \dots + 1 + \sqrt{n} + \sqrt{n}}{n} \ge n^{1/n} \ge 1
1 - \frac{2}{n} + \frac{2}{\sqrt{n}} \ge n^{1/n} \ge 1
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