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. $$\sum_{n=1}^\infty 3(0.75)^n =$$

   (a) $9$
   (b) $12$
   (c) $\infty$
   (d) $4$

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3. 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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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. 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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