Question

Find the interval and radius of convergence for the given power series. (1) $\sum_{n=1}^{\infty} \frac{2^n}{n} x^n$ (2) $\sum_{n=1}^{\infty} \frac{5^n}{n!} x^n$ (3) $\sum_{k=1}^{\infty} \frac{1}{k^2 + k} (3x - 1)^k$

Name: find the interval and radius of convergence for the given power series 1 sumn1infty frac2nn xn 2 sumn1infty frac5nn xn 3 sumk1infty frac1k2 k 3x 1k 97679
Uploaded: 2024-04-24T14:36:58-08:00
Duration: 3 min 10 s
Channel: Keondre Parker
Description: find the interval and radius of convergence for the given power series 1 sumn1infty frac2nn xn 2 sumn1infty frac5nn xn 3 sumk1infty frac1k2 k 3x 1k 97679

          Find the interval and radius of convergence for the given power series.
(1) $\sum_{n=1}^{\infty} \frac{2^n}{n} x^n$
(2) $\sum_{n=1}^{\infty} \frac{5^n}{n!} x^n$
(3) $\sum_{k=1}^{\infty} \frac{1}{k^2 + k} (3x - 1)^k$

$find the interval and radius of convergence for the given power series 1 sumn1infty frac2nn xn 2 sumn1infty frac5nn xn 3 sumk1infty frac1k2 k 3x 1k 97679$

Added by Richard N.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Keondre Parker

04/24/2024

Step 1

The radius of convergence is $R = \frac{1}{2}$. The interval of convergence is $(-\frac{1}{2}, \frac{1}{2})$. We need to check the endpoints. For $x = \frac{1}{2}$, $\sum_{n=1}^{\infty} \frac{2^n}{n} (\frac{1}{2})^n = \sum_{n=1}^{\infty} \frac{1}{n}$, which is the Show more…

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Find the interval and radius of convergence for the given power series. (1) $\sum_{n=1}^{\infty} \frac{2^n}{n} x^n$ (2) $\sum_{n=1}^{\infty} \frac{5^n}{n!} x^n$ (3) $\sum_{k=1}^{\infty} \frac{1}{k^2 + k} (3x - 1)^k$