Sequences Quiz

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1. Find $$\lim_{n \to \infty} 3^{2/n}.$$

   (a) $0$
   (b) $1$
   (c) $3$
   (d) $\infty$

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2. Find $$\lim_{n \to \infty} \dfrac{n^2}{n^2 - 1}.$$

   (a) $1$
   (b) $\dfrac{1}{2}$
   (c) $0$
   (d) $\infty$

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3. Find $$\lim_{n \to \infty} \dfrac{\ln{n}}{n}.$$

   (a) $0$
   (b) $1$
   (c) $\infty$
   (d) $-\infty$

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4. Does $a_n = \sqrt{\dfrac{n+1}{9n+1}}$ converge or diverge? If it converges, find the limit.

   (a) Converges to $\dfrac{1}{9}$
   (b) Converges to $\dfrac{1}{3}$
   (c) Converges to $\dfrac{1}{\sqrt{3}}$
   (d) Diverges

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5. Find the limit, if it exists, of $a_n = \left(\dfrac{n+1}{n}\right)^n$.

   (a) $0$
   (b) $x$
   (c) $\infty$
   (d) $e$

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