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Practice: Power Series Representation
Related Topics
Wize University Calculus 2 Textbook > Power Series
Functions and Power Series
8 Activities
Practice: Power Series Representation
Find a power series represetnation of
f
(
x
)
=
2
x
−
1
1
−
x
2
f(x)=\frac{2x-1}{1-x^2}
f
(
x
)
=
1
−
x
2
2
x
−
1
and determine the radius of convergece.
∑
n
=
0
∞
[
1
2
+
3
(
−
1
)
n
2
]
x
n
{\displaystyle \sum_{n=0}^\infty}\left[\frac{1}{2}+\frac{3(-1)^n}{2}\right]x^n
n
=
0
∑
∞
[
2
1
+
2
3
(
−
1
)
n
]
x
n
; Radius of convergence is
R
=
1
2
R=\frac{1}{2}
R
=
2
1
∑
n
=
0
∞
[
1
2
−
3
(
−
1
)
n
2
]
x
n
{\displaystyle \sum_{n=0}^\infty}\left[\frac{1}{2}-\frac{3(-1)^n}{2}\right]x^n
n
=
0
∑
∞
[
2
1
−
2
3
(
−
1
)
n
]
x
n
; Radius of convergence is
R
=
1
R=1
R
=
1
∑
n
=
0
∞
[
3
(
−
1
)
n
2
]
x
n
{\displaystyle \sum_{n=0}^\infty}\left[\frac{3(-1)^n}{2}\right]x^n
n
=
0
∑
∞
[
2
3
(
−
1
)
n
]
x
n
; Radius of convergence is
R
=
1
R=1
R
=
1
∑
n
=
0
∞
[
3
2
−
3
(
−
1
)
n
2
]
x
n
{\displaystyle \sum_{n=0}^\infty}\left[\frac{3}{2}-\frac{3(-1)^n}{2}\right]x^n
n
=
0
∑
∞
[
2
3
−
2
3
(
−
1
)
n
]
x
n
; Radius of convergence is
R
=
1
2
R=\frac{1}{2}
R
=
2
1
∑
n
=
0
∞
[
3
2
+
3
(
−
1
)
n
2
]
x
n
{\displaystyle \sum_{n=0}^\infty}\left[\frac{3}{2}+\frac{3(-1)^n}{2}\right]x^n
n
=
0
∑
∞
[
2
3
+
2
3
(
−
1
)
n
]
x
n
; Radius of convergence is
R
=
1
R=1
R
=
1
I don't know
Check Submission
More Functions and Power Series Questions:
Practice: Power Series Representation
Find a power series represetnation of
f
(
x
)
=
2
x
−
1
1
−
x
2
f(x)=\frac{2x-1}{1-x^2}
f
(
x
)
=
1
−
x
2
2
x
−
1
and determine the radius of convergece.
Practice: Power Series Representation
Practice: Power Series Representation
Find a power series represetnation of
f
(
x
)
=
2
x
−
1
1
−
x
2
f(x)=\frac{2x-1}{1-x^2}
f
(
x
)
=
1
−
x
2
2
x
−
1
and determine the radius of convergece.
Practice: Power Series Representation
Practice: Power Series Representation
Find a power series represetnation of
f
(
x
)
=
2
x
−
1
1
−
x
2
f(x)=\frac{2x-1}{1-x^2}
f
(
x
)
=
1
−
x
2
2
x
−
1
and determine the radius of convergece.
Practice: Power Series Representation
Practice: Power Series Representation
Find a power series represetnation of
f
(
x
)
=
2
x
−
1
1
−
x
2
f(x)=\frac{2x-1}{1-x^2}
f
(
x
)
=
1
−
x
2
2
x
−
1
and determine the radius of convergece.
Practice: Power Series Representation
Practice: Power Series Representation
Find a power series represetnation of
f
(
x
)
=
2
x
−
1
1
−
x
2
f(x)=\frac{2x-1}{1-x^2}
f
(
x
)
=
1
−
x
2
2
x
−
1
and determine the radius of convergece.
Practice: Integrating a Power Series*
Practice: Power Series Representation
Find a power series represetnation of
f
(
x
)
=
x
arctan
x
2
f(x)=x\ \arctan x^2
f
(
x
)
=
x
arctan
x
2
and determine the radius of convergece.
Practice: Power Series Representation
Practice: Power Series Representation
Find a power series represetnation of
f
(
x
)
=
2
x
−
1
1
−
x
2
f(x)=\frac{2x-1}{1-x^2}
f
(
x
)
=
1
−
x
2
2
x
−
1
and determine the radius of convergece.