Power Series: Radius, Interval of Convergence
AP Calculus BC · Flashcards
AP CALCULUS BC · FLASHCARDS
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QUESTION
What does the radius of convergence
R
=
∞
R = \text{∞}
R
=
∞
imply?
QUESTION
What is the interval of convergence for a power series?
QUESTION
Determine the interval of convergence for
∑
n
=
1
∞
(
−
1
)
n
x
n
n
\textstyle\sum_{n=1}^{\infty} \frac{(-1)^n x^n}{n}
∑
n
=
1
∞
n
(
−
1
)
n
x
n
.
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ANSWER
(
−
1
,
1
]
(-1, 1]
(
−
1
,
1
]
. Alternating series converges at
x
=
1
x = 1
x
=
1
; diverges at
x
=
−
1
x = -1
x
=
−
1
.
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