Problem

Find a power series representation for the functi…

02:17

Problem 16 Easy Difficulty

Find a power series representation for the function and determine the radius of convergence.
$ f(x) = x^2 \tan^{-1} (x^3) $

Answer

$\sum_{n=0}^{\infty}(-1)^{n} \frac{x^{6 n+5}}{2 n+1}, \quad R=1$

Topics

Sequences

Series

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 9

Representations of Functions as Power Series

Discussion

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Video Transcript

Okay, So fun. The power Siri's for death backs and determine its readers of convergence. All right, so we can first, if spend these attendants of x Q part. So this is equal to and from zero to infinity and X cube to the power of to most wanna words who minus one times nothing wanted power from minus What? And we know that we knew it from the Taylor Siri's of octane in X. The riches of convergence is just articles one. And so this is gonna be seen with five to and from one suing for the X to the power of six and miners, three plus two is minus one over two months. One times ninety one off on minus one. All right.

Yiming Z.

University of Illinois at Urbana-Champaign