AP Calculus BC Quiz
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INFINITE SEQUENCES AND SERIES
Question 1
of 20
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A physics model includes
∑
n
=
1
∞
(
−
1
)
n
+
1
1
n
!
\sum_{n=1}^{\infty}(-1)^{n+1}\frac{1}{n!}
∑
n
=
1
∞
(
−
1
)
n
+
1
n
!
1
. Does the series converge?
A
Diverges because factorials grow too slowly.
B
Converges by the Alternating Series Test because
1
n
!
\frac{1}{n!}
n
!
1
decreases and approaches
0
0
0
.
C
Diverges because
lim
n
→
∞
1
n
!
=
1
\lim_{n\to\infty}\frac{1}{n!}=1
lim
n
→
∞
n
!
1
=
1
.
D
Converges because
1
n
!
\frac{1}{n!}
n
!
1
is increasing.
E
Diverges because
∑
1
n
!
\sum \frac{1}{n!}
∑
n
!
1
diverges.
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