Comparison Tests for Convergence
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
Identify a series to compare with
3
n
3
+
ln
(
n
)
\frac{3}{n^3 + \text{ln}(n)}
n
3
+
ln
(
n
)
3
.
QUESTION
Use Comparison: does
n
2
+
3
n
3
+
1
\frac{n^2 + 3}{n^3 + 1}
n
3
+
1
n
2
+
3
converge?
QUESTION
Use Comparison: is
1
n
0.5
\frac{1}{n^{0.5}}
n
0.5
1
convergent?
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ANSWER
Diverges; compare to
1
n
0.5
\frac{1}{n^{0.5}}
n
0.5
1
(divergent
p
p
p
-series).
p
=
0.5
<
1
p = 0.5 < 1
p
=
0.5
<
1
makes this a divergent
p
p
p
-series.
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