Problem #PRU-61486

Let $(1 + \sqrt{2} + \sqrt{3})^{n} = p_{n} + q_{n} \sqrt{2} + r_{n} \sqrt{3} + s_{n} \sqrt{6}$ for $n \geq 0$ . Find:

a) $lim_{n \to \infty} \frac{p_{n}}{q_{n}}$ ; b) $lim_{n \to \infty} \frac{p_{n}}{r_{n}}$ ; c) $lim_{n \to \infty} \frac{p_{n}}{s_{n}}$ ;

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