Find the radius of convergence, R, of the series.Σ3"n4n- 1R = 3Find the interval, I, of convergence of the series. (Enter your answer using interval notation.)I =

Answered: Find the radius of convergence, R, of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Find the radius of convergence, R, of the series.
Σ
3"n4
n- 1
R = 3
Find the interval, I, of convergence of the series. (Enter your answer using interval notation.)
I =

Expert Solution

Step 1

In this question, concept of Radius of convergence is applied.

Radius of convergence

The radius of convergence of a power series is the diameter of the greatest disc in which the series converges in mathematics. It's either a positive real number or $\infty$ . The power series converges absolutely and uniformly on compact sets inside the open disc of radius equal to the radius of convergence when it is positive, and the Taylor series of the analytic function is the Taylor series to which it converges.The distance from $a$ to the nearest point where $f$ cannot be specified in a fashion that renders it holomorphic is equal to the radius of convergence of a power series $f$ centred on a point $a$ .