Συντηρη n=1

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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Real Analysis II: For the power series, find the radius of convergence R and interval of convergence (IOC) Kindly find steps/examples for guide in photo II
Συντήρη
n=1
Transcribed Image Text:Συντήρη n=1
EX.
(Boundary
points
=
So (im |an| = lim |+|
ns anti
EX. Find R.O.C. Notice an =
and R=1. check Xx=1:
=
check x = -1 = f(x) = f(-1) = 28 (-1) ² = 1 - 1 + |-|-|-=-=-
C = (-1, 1)
n=0
Div.
16-09. Def f(x) = & an x^² = a + ax+ 9₂x² + 93x²³ +-... is
não
a power
Series
Goal: Find the
domain
Thm: Lef & anx^ be a power Series
if X ERH
no
L
Let R.
=
Then
n=1
an
∞
∞ if x = 0
to
if
Eanx Conv. abs.
Eanx div.
If R =∞, then Eanxn Conv. abs. #XER
If R=0, then Eanx" Conv. only for X ²0
find the
an
of f(x) - (the x's for which som
Eanx Conv.)
I'm suplanta
lim
n=∞an+1
Let X=1. Then & I
n=1 n
กร
if
if Ix > Re R
R.O.C.
lim
336
XnE+
n=1
Let x=-1. Then Ex^²=(-1)^
<= [¹,1)
naln
1x1 <RE R+ and
n
n+l
x "C
lim
A-B
Dive,
7+1
n
Harmonic
R.O.C
Can => 0
n
Conv. by AST lim 1=0, an = 1/
zn
= antl
Transcribed Image Text:EX. (Boundary points = So (im |an| = lim |+| ns anti EX. Find R.O.C. Notice an = and R=1. check Xx=1: = check x = -1 = f(x) = f(-1) = 28 (-1) ² = 1 - 1 + |-|-|-=-=- C = (-1, 1) n=0 Div. 16-09. Def f(x) = & an x^² = a + ax+ 9₂x² + 93x²³ +-... is não a power Series Goal: Find the domain Thm: Lef & anx^ be a power Series if X ERH no L Let R. = Then n=1 an ∞ ∞ if x = 0 to if Eanx Conv. abs. Eanx div. If R =∞, then Eanxn Conv. abs. #XER If R=0, then Eanx" Conv. only for X ²0 find the an of f(x) - (the x's for which som Eanx Conv.) I'm suplanta lim n=∞an+1 Let X=1. Then & I n=1 n กร if if Ix > Re R R.O.C. lim 336 XnE+ n=1 Let x=-1. Then Ex^²=(-1)^ <= [¹,1) naln 1x1 <RE R+ and n n+l x "C lim A-B Dive, 7+1 n Harmonic R.O.C Can => 0 n Conv. by AST lim 1=0, an = 1/ zn = antl
Expert Solution
Step 1

We will use the fact that a series an  will be convergence if an+1an<1

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