Geometric Series Quiz

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1. Is $\sum_{n=3}^\infty \dfrac{3^n}{2^{2n}}$ convergent or divergent? If it is convergent, find its sum.

   (a) $\frac{27}{64}$
   (b) $\frac{27}{16}$
   (c) $4$
   (d) $3$

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2. Does $\sum_{n=1}^\infty (\tan{7})^n$ converge or diverge?

   (a) Converges since $\tan{7} > 1$
   (b) Converges since $0 < \tan{7} < 1$
   (c) Diverges since $\tan{7} > 1$
   (d) Diverges since $0 < \tan{7} < 1$

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3. Write $0.83838383\ldots$ as a reduced fraction.

   (a) $\dfrac{83}{100}$
   (b) $\dfrac{83}{99}$
   (c) $\dfrac{71}{85}$
   (d) $\dfrac{166}{198}$

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4. $$\sum_{n=1}^\infty \dfrac{6^{n+2}}{2^{3n}} =$$

   (a) $108$
   (b) $27$
   (c) $\dfrac{4}{3}$
   (d) $\infty$

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5. Write $0.997997997\ldots$ as a reduced fraction.

   (a) $\dfrac{997}{1000}$
   (b) $\dfrac{997}{999}$
   (c) $\dfrac{2991}{2997}$
   (d) $\dfrac{996}{999}$

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