Question

Select all the series below that must converge if a power series $sum_{n=0}^{infty} a_n x^n$ has radius of convergence 8. $sum_{n=0}^{infty} a_n 7^n$ $sum_{n=0}^{infty} a_n (-7)^n$ $sum_{n=0}^{infty} a_n 9^n$ $sum_{n=0}^{infty} a_n (-9)^n$ $sum_{n=0}^{infty} a_n 8^n$ $sum_{n=0}^{infty} a_n (-8)^n$

          Select all the series below that must converge if a power series $sum_{n=0}^{infty} a_n x^n$ has radius of convergence 8.
$sum_{n=0}^{infty} a_n 7^n$
$sum_{n=0}^{infty} a_n (-7)^n$
$sum_{n=0}^{infty} a_n 9^n$
$sum_{n=0}^{infty} a_n (-9)^n$
$sum_{n=0}^{infty} a_n 8^n$
$sum_{n=0}^{infty} a_n (-8)^n$

Select all the series below that must converge if a power series sumn=0^infty an x^n has radius of convergence 8.
sumn=0^infty an 7^n
sumn=0^infty an (-7)^n
sumn=0^infty an 9^n
sumn=0^infty an (-9)^n
sumn=0^infty an 8^n
sumn=0^infty an (-8)^n

Added by David B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Diogo Caetano

11/18/2022

Step 1

**Step 2:** Given that the radius of convergence is $r = 8$, we need to determine which series will definitely converge within the range $|x| < 8$. **Step 3:** The series that must converge are: Show more…

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Select all the series below that must converge if a power series sum n=0 to infinity an x^n has radius of convergence 8. sum n=0 to infinity an 7^n, sum n=0 to infinity an (-7)^n, sum n=0 to infinity an 9^n, sum n=0 to infinity an (-9)^n, sum n=0 to infinity an 8^n, sum n=0 to infinity an (-8)^n