Select ALL the statements that are true for a power series E-o Cn (x – a)". in=0 No matter what the coefficients Cn are - the power series converges for x = a. Cn+1 If the limit lim Cn < 1, then the power series always converges for any x. n→∞ O If a 5 and the radius of convergence is R = 2 then the power series converges for x = 6. We can only study the convergence of the power series for x > a.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
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Question 1
Select ALL the statements that are true for a power series E, Cn (x – a)".
n=0
No matter what the coefficients Cn are - the power series converges for x = a.
Сп+1
If the limit lim
Cn
< 1, then the power series always converges for any x.
O If a = 5 and the radius of convergence is R=2 then the power series converges for
x = 6.
We can only study the convergence of the power series for x > a.
Transcribed Image Text:Question 1 Select ALL the statements that are true for a power series E, Cn (x – a)". n=0 No matter what the coefficients Cn are - the power series converges for x = a. Сп+1 If the limit lim Cn < 1, then the power series always converges for any x. O If a = 5 and the radius of convergence is R=2 then the power series converges for x = 6. We can only study the convergence of the power series for x > a.
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