Geometric Series Quiz

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1. 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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2. $$\sum_{n=0}^\infty \dfrac{1}{2^n} =$$

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

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3. $$\sum_{n=3}^\infty \sqrt{3}^n2^{1-n} =$$

   (a) $\dfrac{9}{2}$
   (b) $\dfrac{3\sqrt{3}}{8 - 4\sqrt{3}}$
   (c) $\dfrac{3\sqrt{3}}{4 - 2\sqrt{3}}$
   (d) $\infty$

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

   (a) $5$
   (b) $20$
   (c) $\dfrac{5}{4}$
   (d) $\infty$

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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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