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2016 AIME Problems
1
Geometric Series Equations
Geometric Series Equations
Source: 2016 AIME I #1
March 4, 2016
2016 AIME I
AIME
geometric series
Problem Statement
For
−
1
<
r
<
1
-1 < r < 1
−
1
<
r
<
1
, let
S
(
r
)
S(r)
S
(
r
)
denote the sum of the geometric series
12
+
12
r
+
12
r
2
+
12
r
3
+
…
.
12 + 12r + 12r^2 + 12r^3 + \ldots.
12
+
12
r
+
12
r
2
+
12
r
3
+
…
.
Let
a
a
a
between
−
1
-1
−
1
and
1
1
1
satisfy
S
(
a
)
S
(
−
a
)
=
2016
S(a)S(-a)=2016
S
(
a
)
S
(
−
a
)
=
2016
. Find
S
(
a
)
+
S
(
−
a
)
S(a) + S(-a)
S
(
a
)
+
S
(
−
a
)
.
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