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 $\sum_{n=1}^\infty \left(\dfrac{-e}{\pi}\right)^n$ converge?

   (a) Diverges since $-1 < -e/\pi < 0$
   (b) Diverges since $-e/\pi < -1$
   (c) Converges since $-e/\pi < -1$
   (d) Converges since $-1 < -e/\pi < 0$

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

   (a) $6$
   (b) $\infty$
   (c) $\dfrac{1}{4}$
   (d) $\dfrac{3}{16}$

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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. 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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