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. $$\sum_{n=0}^\infty \dfrac{6^n}{7^n} =$$

   (a) $\infty$
   (b) $\dfrac{49}{6}$
   (c) $7$
   (d) $6$

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3. Compute $2 - \frac{2}{3} + \frac{2}{9} - \frac{2}{27} + \ldots$.

   (a) $\dfrac{6}{5}$
   (b) $\infty$
   (c) $\dfrac{3}{2}$
   (d) $-\infty$

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4. Find the sum $\sum_{n=1}^\infty \dfrac{9^n}{9^{n+4}}$.

   (a) $1$
   (b) $\infty$
   (c) $\dfrac{1}{9^4}$
   (d) $9^4$

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5. Does $\sum_{n=1}^\infty \dfrac{2^{3n}}{7^{n+1}}$ converge or diverge?

   (a) Diverges since $8/7 < 1$
   (b) Diverges since $8/7 > 1$
   (c) Converges since $2/7 < 1$
   (d) Converges since $8/14 < 1$

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