Sequences Quiz

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

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

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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 $a_n = (-1)^n$ 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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5. Let $a_n = \dfrac{3 + \sin{\left(n\right)}}{\sqrt{n}}$. Find $\lim_{n \to \infty} a_n$.

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

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