Representing Series as Power Series
AP Calculus BC · Flashcards
AP CALCULUS BC · FLASHCARDS
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QUESTION
Convert
Sum
=
x
n
3
n
\text{Sum} = \frac{x^n}{3^n}
Sum
=
3
n
x
n
into a power series centered at 1.
QUESTION
What is the interval of convergence for
1
+
x
+
x
2
+
...
1 + x + x^2 + \text{...}
1
+
x
+
x
2
+
...
?
QUESTION
Determine the radius of convergence for
Sum
=
(
2
x
)
n
\text{Sum} = (2x)^n
Sum
=
(
2
x
)
n
.
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ANSWER
R
=
1
2
R = \frac{1}{2}
R
=
2
1
. Series
∑
(
2
x
)
n
\sum (2x)^n
∑
(
2
x
)
n
has radius
1
2
\frac{1}{2}
2
1
from ratio test.
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