Numerade

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Entered Answer Preview 0.25 0.25 \( (-8.25,-7.75) \) \[ (-8.25,-7.75) \] At least one of the answers above is NOT correct. Consider the power series \[ \sum_{n=1}^{\infty} \frac{(-4)^{n}}{\sqrt{n}}(x+8)^{n} . \] Find the radius of convergence \( R \). If it is infinite, type "infinity" or "inf". Answer: \( R=0.25 \) What is the interval of convergence? Answer (in interval notation): \( (-8.25,-7.75) \)

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INSTANT ANSWER

\begin{tabular}{|l|l|l|l|} \hline Entered & Answer Preview & Result & Message \\ \hline\( (-0.25,0.25] \) & \( \left(\frac{-1}{4}, \frac{1}{4}\right] \) & incorrect & The type of interval is incorrect \\ \hline \end{tabular} The answer above is NOT correct. Consider the series \[ \sum_{n=1}^{\infty} \frac{(4 x)^{n}}{n} \] Find the interval of convergence of this power series by first using the ratio test to find its radius of convergence and then testing the series' behavior at the endpoints of the interval specified by the radius of convergence. interval of convergence \( =(-1 / 4,1 / 4] \)

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INSTANT ANSWER

Consider the power series \[ \sum_{n=1}^{\infty} \frac{(3 x-1)^{n}}{n^{2}} \] Find the radius of convergence \( R \). If it is infinite, type "infinity" or "inf". Answer: \( R= \) What is the interval of convergence? Answer (in interval notation):

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INSTANT ANSWER

Consider the power series \[ \sum_{n=1}^{\infty} \frac{(-4)^{n}}{\sqrt{n}}(x+8)^{n} . \] Find the radius of convergence \( R \). If it is infinite, type "infinity" or "inf". Answer: \( R= \) What is the interval of convergence? Answer (in interval notation):

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INSTANT ANSWER

Consider the series \[ \sum_{n=1}^{\infty} \frac{(4 x)^{n}}{n} \] Find the interval of convergence of this power series by first using the ratio test to find its radius of convergence and then testing the series' behavior at the endpoints of the interval specified by the radius of convergence. interval of convergence \( = \) (Enter your answer as an interval: thus, if the interval of convergence were \( -3<x \leq 5 \), you would enter \( \mathbf{( - 3 , 5 ]} \). Use Inf for any endpoint at infinity.)

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Consider the power series \[ \sum_{n=1}^{\infty} \frac{7^{n} x^{n}}{n !} \] Find the radius of convergence \( R \). If it is infinite, type "infinity" or "inf". Answer: \( R= \) What is the interval of convergence? Answer (in interval notation):

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Consider the power series \[ \sum_{n=1}^{\infty} \frac{(-1)^{n} x^{n}}{\sqrt{n+3}} \] Find the radius of convergence \( R \). If it is infinite, type "infinity" or "inf". Answer: \( R= \) What is the interval of convergence? Answer (in interval notation):

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Find all the values of \( x \) such that the given series would converge. \[ \sum_{n=1}^{\infty} \frac{(-1)^{n} x^{n}}{11^{n}\left(n^{2}+11\right)} \] The series is convergent from \( x= \) , left end included (enter \( \mathrm{Y} \) or \( \mathrm{N} \) ): to \( x= \) , right end included (enter \( \mathrm{Y} \) or \( \mathrm{N} \) ):

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INSTANT ANSWER

Match each of the power series with its interval of convergence. 1. \( \sum_{n=1}^{\infty} \frac{n !(9 x-4)^{n}}{4^{n}} \) 2. \( \sum_{n=1}^{\infty} \frac{(x-4)^{n}}{(4)^{n}} \) 3. \( \sum_{n=1}^{\infty} \frac{(9 x)^{n}}{n^{4}} \) 4. \( \sum_{n=1}^{\infty} \frac{(x-4)^{n}}{(n !) 4^{n}} \) A. \( (0,8) \) B. \( (-\infty, \infty) \) C. \( \left[\frac{-1}{9}, \frac{1}{9}\right] \) D. \( \left\{\frac{4}{9}\right\} \)

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INSTANT ANSWER

Match each of the following with the correct statement. A. The series is absolutely convergent. C. The series converges, but is not absolutely convergent. D. The series diverges. 1. \( \sum_{n=1}^{\infty} \frac{(n+1)\left(4^{2}-1\right)^{n}}{4^{2 n}} \) 2. \( \sum_{n=1}^{\infty} \frac{(-1)^{n}}{2 n+2} \) 3. \( \sum_{n=1}^{\infty}(-1)^{n} \frac{\sqrt{n}}{n+3} \) 4. \( \sum_{n=1}^{\infty} \frac{(-2)^{n}}{n^{2}} \) 5. \( \sum_{n=1}^{\infty} \frac{\sin (5 n)}{n^{2}} \)

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