Blumenfeld Calc
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Power Series Quiz
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Compute the interval of convergence for $f(x) = \sum_{n=1}^\infty \dfrac{(x-2)^n}{n^3 4^n}$.
(a) $(-2, 6)$
(b) $[-2, 6)$
(c) $(-2, 6]$
(d) $[-2, 6]$
What is the radius of convergence for the power series $\sum_{n=0}^\infty x^n$?
(a) $0$
(b) $1$
(c) $e$
(d) $\infty$
Find a power series representation of $\ln{(1-x)}$ and its radius of convergence.
(a) $-\sum_{n=1}^\infty \dfrac{x^n}{n}, R = \infty$
(b) $-\sum_{n=1}^\infty \dfrac{x^n}{n}, R = 1$
(c) $-\sum_{n=0}^\infty \dfrac{x^n}{n}, R = 1$
(d) $\sum_{n=0}^\infty \dfrac{x^{n+1}}{n+1}, R = 1$
Find the interval of convergence for $f(x) = \sum_{n=1}^\infty \dfrac{(-1)^nx^n(n+4)}{11^n}$.
(a) $(-11, 11)$
(b) $[-11, 11)$
(c) $(-11, 11]$
(d) $[-11, 11]$
Write $\dfrac{3}{1-x^3}$ as a power series. What is the radius of convergence?
(a) $\sum_{n=0}^\infty 3x^n, R = 1$
(b) $\sum_{n=0}^\infty 3x^{3n}, R = 1$
(c) $\sum_{n=1}^\infty 3x^{3n}, R = 1$
(d) $\sum_{n=0}^\infty \dfrac{x^{3n}}{3^{3n-1}}, R = 3$
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