(a) Find the radius of convergence ofan(x − c)n.n=0(b) Find a power series for∞d ∑an(x − c)n,dxn=0and determine its radius of convergence.(c) Find a power series for ∫ ( ∞)∑an(x − c)ndx,n=0and determine its radius of convergence. Question 2 Suppose that the coefficients of the power seriesan(x – c)"n=0satisfy|an+1|lim= L.Jan|n00(a) Find the radius of convergence of >an(x – c)".n=0(b) Find a power series forddr an(x – c)",n=0and determine its radius of convergence.(c) Find a power series foran(x – c)"dx,and determine its radius of convergence.

Answered: Image /qna-images/answer/83c3b92c-c06f-4e25-9cf4-428240d38afd.jpg

Ean(x – c)" - n=0 satisfy |an+1] lim = L. no an (a) Find the radius of convergence of > an(x – c)". n=0 (b) Find a power series for d :Ean(x – c)", dx n=0 and determine its radius of convergence. (c) Find a power series for an(x – c)" | dx, and determine its radius of convergence.

Ean(x – c)" - n=0 satisfy |an+1] lim = L. no an (a) Find the radius of convergence of > an(x – c)". n=0 (b) Find a power series for d :Ean(x – c)", dx n=0 and determine its radius of convergence. (c) Find a power series for an(x – c)" | dx, and determine its radius of convergence.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.3: Geometric Sequences

Problem 49E

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Question

(a) Find the radius of convergence of an(x − c)n. n=0 (b) Find a power series for ∞ d ∑ an(x − c)n, dx n=0 and determine its radius of convergence. (c) Find a power series for ∫ ( ∞) ∑ an(x − c)n dx, n=0 and determine its radius of convergence.