Alternating Series Test for Convergence
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
Does the series
∑
n
=
1
∞
(
−
1
)
n
(
1
+
1
n
2
)
\textstyle\sum_{n=1}^{\infty} (-1)^n (1 + \frac{1}{n^2})
∑
n
=
1
∞
(
−
1
)
n
(
1
+
n
2
1
)
converge?
QUESTION
Determine whether
∑
n
=
1
∞
(
−
1
)
n
n
\textstyle \sum_{n=1}^{\infty} (-1)^n n
∑
n
=
1
∞
(
−
1
)
n
n
converges.
QUESTION
Find if the series
∑
n
=
1
∞
(
−
1
)
n
1
n
5
\textstyle \sum_{n=1}^{\infty} (-1)^n \frac{1}{n^5}
∑
n
=
1
∞
(
−
1
)
n
n
5
1
converges.
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ANSWER
Yes, it converges by the Alternating Series Test. Higher powers guarantee all alternating series test conditions are satisfied.
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