(-1)" 81+n Σ (x – 7)" n + 4 n=0 8. 5.

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# Section 4-14: Power Series - Assignment Problems

For each of the following power series, determine the interval and radius of convergence.

1. \(\sum_{n=0}^{\infty} \frac{6^{1-n}}{(-2)^{3-2n}} (x + 4)^n\)

2. \(\sum_{n=0}^{\infty} \frac{(10x - 1)^n}{n^{3+n}}\)

3. \(\sum_{n=0}^{\infty} \frac{(3n)!}{(2n - 2)!} (6x - 9)^n\)

4. \(\sum_{n=0}^{\infty} \frac{(-1)^n n^2}{4n + 1} (5x + 20)^n\)

5. \(\sum_{n=0}^{\infty} \frac{(-1)^n 8^{1+n}}{n + 4} (x - 7)^n\)
Transcribed Image Text:# Section 4-14: Power Series - Assignment Problems For each of the following power series, determine the interval and radius of convergence. 1. \(\sum_{n=0}^{\infty} \frac{6^{1-n}}{(-2)^{3-2n}} (x + 4)^n\) 2. \(\sum_{n=0}^{\infty} \frac{(10x - 1)^n}{n^{3+n}}\) 3. \(\sum_{n=0}^{\infty} \frac{(3n)!}{(2n - 2)!} (6x - 9)^n\) 4. \(\sum_{n=0}^{\infty} \frac{(-1)^n n^2}{4n + 1} (5x + 20)^n\) 5. \(\sum_{n=0}^{\infty} \frac{(-1)^n 8^{1+n}}{n + 4} (x - 7)^n\)
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