Match each of the following power series with its corresponding interval of convergence: (\sum_{n=1}^{\infty} \frac{(x-5)^n}{n! 5^n}) (\sum_{n=1}^{\infty} \frac{n! (5x-5)^n}{5^n}) (\sum_{n=1}^{\infty} \frac{(5x)^n}{n^5}) (\sum_{n=1}^{\infty} \frac{(x-5)^n}{5^n}) A. ((0, 10)) B. ([-1/5, 1/5]) C. ((-\infty, \infty)) D. ({5/5})

Nov 12, 2024

Find the power series interval of convergence?

Match each of the following power series with its corresponding interval of convergence:

A. ((0, 10))
B. ([-1/5, 1/5])
C. ((-\infty, \infty))
D. ({5/5})

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Nov 24, 2024

You can determine the interval by performing the ratio test on convergence of the series. By this method i get:

1 → C

2 → A

3 → B

4 → D

Steps:

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