AP Calculus BC Quiz
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INFINITE SEQUENCES AND SERIES
Question 1
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Compute
∑
n
=
2
∞
6
(
1
2
)
n
\sum_{n=2}^{\infty} 6\left(\tfrac{1}{2}\right)^n
∑
n
=
2
∞
6
(
2
1
)
n
by treating it as a geometric series.
A
6
1
−
1
2
\tfrac{6}{1-\tfrac{1}{2}}
1
−
2
1
6
B
6
(
1
2
)
2
1
−
1
2
\tfrac{6\left(\tfrac{1}{2}\right)^2}{1-\tfrac{1}{2}}
1
−
2
1
6
(
2
1
)
2
C
6
(
1
2
)
1
−
1
2
\tfrac{6\left(\tfrac{1}{2}\right)}{1-\tfrac{1}{2}}
1
−
2
1
6
(
2
1
)
D
Diverges because it starts at
n
=
2
n=2
n
=
2
E
6
(
1
2
)
2
1
+
1
2
\tfrac{6\left(\tfrac{1}{2}\right)^2}{1+\tfrac{1}{2}}
1
+
2
1
6
(
2
1
)
2
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