Power Series: Radius, Interval of Convergence
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
Identify the radius of convergence for
a
n
=
1
n
2
a_n = \frac{1}{n^2}
a
n
=
n
2
1
using the ratio test.
QUESTION
Identify the radius of convergence for
∑
n
=
0
∞
2
n
x
n
\sum_{n=0}^{\infty} 2^n x^n
∑
n
=
0
∞
2
n
x
n
.
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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