AP Calculus BC Quiz
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INFINITE SEQUENCES AND SERIES
Question 1
of 20
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For the series
∑
n
=
1
∞
3
n
n
!
\sum_{n=1}^{\infty} \frac{3^n}{n!}
∑
n
=
1
∞
n
!
3
n
, what does the ratio test conclude about convergence?
A
Diverges because the ratio-test limit is
3
>
1
3>1
3
>
1
B
Converges absolutely because the ratio-test limit is
0
<
1
0<1
0
<
1
C
Inconclusive because the ratio-test limit is
1
1
1
D
Diverges because the ratio-test limit is
∞
\infty
∞
E
Converges absolutely because the ratio-test limit is
1
3
<
1
\tfrac{1}{3}<1
3
1
<
1
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