Ratio Test for Convergence
AP Calculus BC · Flashcards
AP CALCULUS BC · FLASHCARDS
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QUESTION
What does the Ratio Test say about
a
n
=
1
(
n
+
1
)
!
a_n = \frac{1}{(n+1)!}
a
n
=
(
n
+
1
)!
1
?
QUESTION
Is
a
n
=
1
2
n
a_n = \frac{1}{2^n}
a
n
=
2
n
1
convergent by the Ratio Test?
QUESTION
Evaluate
a
n
=
n
3
n
!
a_n = \frac{n^3}{n!}
a
n
=
n
!
n
3
using the Ratio Test. Convergent or divergent?
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ANSWER
Convergent.
L
=
(
n
+
1
)
3
n
3
⋅
1
n
+
1
=
(
n
+
1
)
2
n
3
→
0
<
1
L = \frac{(n+1)^3}{n^3} \cdot \frac{1}{n+1} = \frac{(n+1)^2}{n^3} \to 0 < 1
L
=
n
3
(
n
+
1
)
3
⋅
n
+
1
1
=
n
3
(
n
+
1
)
2
→
0
<
1
.
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