Geometric Series Quiz

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1. $$\sum_{n=2}^\infty \dfrac{3^n}{3^{n+4}} =$$

   (a) $\dfrac{1}{3^4}$
   (b) $3^4$
   (c) $1$
   (d) $\infty$

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2. Does $\sum_{n=2}^\infty (\sqrt{2})^n$ converge or diverge?

   (a) Diverges since $\sqrt{2} < 1$
   (b) Diverges since $\sqrt{2} > 1$
   (c) Converges since $\sqrt{2} < 1$
   (d) Converges since $\sqrt{2} > 1$

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3. Compute $\sum_{n=1}^\infty \dfrac{4^n + 2^n}{5^n}$.

   (a) $\dfrac{14}{3}$
   (b) $\dfrac{58}{15}$
   (c) $\infty$
   (d) $\dfrac{20}{3}$

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4. Find the sum $\frac{2}{5} + \frac{2}{25} + \frac{2}{125} + \frac{2}{625} + \ldots$.

   (a) $\dfrac{5}{4}$
   (b) $\infty$
   (c) $\dfrac{1}{5}$
   (d) $\dfrac{1}{2}$

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5. Does $\sum_{n=1}^\infty \cos{(n\pi)}$ converge?

   (a) Converges since $\cos{(n\pi)} < 1$
   (b) Converges by the rational root theorem
   (c) Diverges since $\cos{(n\pi)} = (-1)^n$
   (d) Diverges since $\cos{(n\pi)} > 1$

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