Determining Absolute or Conditional Convergence
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
Determine convergence:
∑
n
=
1
∞
(
−
1
)
n
n
2
\sum_{n=1}^{\infty} \frac{(-1)^n}{n^2}
∑
n
=
1
∞
n
2
(
−
1
)
n
.
QUESTION
Determine convergence:
∑
n
=
1
∞
(
−
1
)
n
n
\sum_{n=1}^{\infty} \frac{(-1)^n}{\sqrt{n}}
∑
n
=
1
∞
n
(
−
1
)
n
.
QUESTION
Apply the Root Test:
∑
n
=
1
∞
(
n
n
+
1
)
n
\sum_{n=1}^{\infty} \left(\frac{n}{n+1}\right)^n
∑
n
=
1
∞
(
n
+
1
n
)
n
.
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ANSWER
Diverges. Root approaches 1, so diverges.
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