Sequences Quiz

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1. Does $a_n = (-1)^n$ converge or diverge? Why?

   (a) Converges by the Monotone Convergence Theorem
   (b) Converges for another reason
   (c) Diverges because it cycles back and forth between $-1$ and $1$
   (d) Diverges to $\pm \infty$

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2. Find the 5th term of $\{\sqrt{n}\}_{n=1}^\infty$.

   (a) $\sqrt{4}$
   (b) $\sqrt{5}$
   (c) $\sqrt{6}$
   (d) $5$

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3. Find $$\lim_{n \to \infty} \ln{(2n + 1)} - \ln{(n-1)}.$$

   (a) $0$
   (b) $\ln{2}$
   (c) $\infty$
   (d) $-\infty$

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

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

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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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