Power Series Quiz

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1. Find the interval of convergence of $\sum_{n=0}^\infty \dfrac{(-1)^nn(x-4)^n}{2^n}$.

   (a) $[2, 6]$
   (b) $(2, 6]$
   (c) $[2, 6)$
   (d) $(2, 6)$

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2. Write $\dfrac{1}{1 - 2x}$ as a power series.

   (a) $\sum_{n=0}^\infty x^{2n}$
   (b) $\sum_{n=0}^\infty 2^{2n}x^{2n}$
   (c) $\sum_{n=0}^\infty 2^nx^n$
   (d) $\sum_{n=0}^\infty x^n$

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3. Compute the interval of convergence for $\sum_{n=1}^\infty \dfrac{(n+3)!(x+2)^n}{4^n}$.

   (a) $(-6, 2)$
   (b) $\{0\}$
   (c) $\{-2\}$
   (d) $(-\infty, \infty)$

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4. Find the interval of convergence of $\sum_{n=0}^\infty \dfrac{(x-1)^n}{n+5}$.

   (a) $(0, 2)$
   (b) $[0, 2)$
   (c) $(0, 2]$
   (d) $[0, 2]$

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5. Write $\dfrac{1}{1 - 5x}$ as a power series. What is the radius of convergence?

   (a) $\sum_{n=0}^\infty 5^nx^n, \dfrac{1}{5}$
   (b) $\sum_{n=0}^\infty \dfrac{x^n}{5^n}, 5$
   (c) $\sum_{n=1}^\infty 5^nx^n, \dfrac{1}{5}$
   (d) $\sum_{n=0}^\infty x^n, 1$

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