1. If the radius of convergence of the power series E-0 Cnx" is 10, what is the radius of convergence of the series En=1 nc,x"-? Why?

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.4: Series And Their Notations
Problem 10TI: Determine whether the sum of the infinite series is defined. 24+(12)+6+(3)+
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Now we integrate term
- This example demonstrates one way
in which power series representations
are useful. Integrating 1/(1 + x) by
hand is incredibly difficult. Different
computer algebra systems return differ-
ent forms of the answer, but they are all
extremely complicated. (If you have a
CAS, try it yourself.) The infinite series
answer that we obtain in Example 8 is
actually much easier to deal with than
the finite answer provided by a CAS.
This series converges
8.6
EXERCISES
1. If the radius of convergence of the power series E-o Cnx"
is 10, what is the radius of convergence of the series
E=1 nc,x"-1? Why?
a legigino
2. Suppose you know that the series E-o bnx" converges for
|x|< 2. What can you say about the following series? Why
bn
Σ
vd zohoz boiupon +1
n=0
slqmexa ni bhN6
3-10 - Find a power series representation for the function an
determine the interval of convergence.
1
3. f(x) =
f(x)
Transcribed Image Text:Now we integrate term - This example demonstrates one way in which power series representations are useful. Integrating 1/(1 + x) by hand is incredibly difficult. Different computer algebra systems return differ- ent forms of the answer, but they are all extremely complicated. (If you have a CAS, try it yourself.) The infinite series answer that we obtain in Example 8 is actually much easier to deal with than the finite answer provided by a CAS. This series converges 8.6 EXERCISES 1. If the radius of convergence of the power series E-o Cnx" is 10, what is the radius of convergence of the series E=1 nc,x"-1? Why? a legigino 2. Suppose you know that the series E-o bnx" converges for |x|< 2. What can you say about the following series? Why bn Σ vd zohoz boiupon +1 n=0 slqmexa ni bhN6 3-10 - Find a power series representation for the function an determine the interval of convergence. 1 3. f(x) = f(x)
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