Geometric Series Quiz

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

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

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3. $$\sum_{n=1}^\infty \dfrac{6^n + 2^n}{7^n} =$$

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

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4. 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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5. 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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