Question

The function $f(x) = \frac{10}{1 + 36x^2}$ is represented as a power series $f(x) = \sum_{n=0}^{\infty} c_n x^n$. Find the first few coefficients in the power series. $c_0 = $ $c_1 = $ $c_2 = $ $c_3 = $ $c_4 = $ Find the radius of convergence $R$ of the series. $R = $

Name: the function fx frac101 36x2 is represented as a power series fx sumn0infty cn xn find the first few coefficients in the power series c0 c1 c2 c3 c4 find the radius of convergence r o 82187
Uploaded: 2022-06-18T17:01:00-08:00
Duration: 4 min 24 s
Channel: Zhumagali Shomanov
Description: the function fx frac101 36x2 is represented as a power series fx sumn0infty cn xn find the first few coefficients in the power series c0 c1 c2 c3 c4 find the radius of convergence r o 82187

          The function $f(x) = \frac{10}{1 + 36x^2}$ is represented as a power series
$f(x) = \sum_{n=0}^{\infty} c_n x^n$.
Find the first few coefficients in the power series.
$c_0 = $
$c_1 = $
$c_2 = $
$c_3 = $
$c_4 = $
Find the radius of convergence $R$ of the series.
$R = $

$the function fx frac101 36x2 is represented as a power series fx sumn0infty cn xn find the first few coefficients in the power series c0 c1 c2 c3 c4 find the radius of convergence r o 82187$

Added by Laura S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Zhumagali Shomanov

06/18/2022

Step 1

We rewrite $f(x)$ as: $f(x) = 10 \cdot \frac{1}{1 + 36x^2} = 10 \cdot \frac{1}{1 - (-36x^2)} = 10 \sum_{n=0}^{\infty} (-36x^2)^n = 10 \sum_{n=0}^{\infty} (-36)^n x^{2n}$ This is valid for $|-36x^2| < 1$, which means $|x^2| < \frac{1}{36}$, so $|x| < \frac{1}{6}$. Show more…

Show all steps

Thanks for your feedback!

The function $f(x) = \frac{10}{1 + 36x^2}$ is represented as a power series $f(x) = \sum_{n=0}^{\infty} c_n x^n$. Find the first few coefficients in the power series. $c_0 = $ $c_1 = $ $c_2 = $ $c_3 = $ $c_4 = $ Find the radius of convergence $R$ of the series. $R = $