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2014 AIME Problems
7
Scary Sums and Logs
Scary Sums and Logs
Source: 2014 AIME II Problem #7
March 27, 2014
trigonometry
logarithms
AMC
sums
AIME
AIME II
2014 AIME II
Problem Statement
Let
f
(
x
)
=
(
x
2
+
3
x
+
2
)
cos
(
π
x
)
f(x) = (x^2+3x+2)^{\cos(\pi x)}
f
(
x
)
=
(
x
2
+
3
x
+
2
)
c
o
s
(
π
x
)
. Find the sum of all positive integers
n
n
n
for which
∣
∑
k
=
1
n
log
10
f
(
k
)
∣
=
1.
\left| \sum_{k=1}^n \log_{10} f(k) \right| = 1.
k
=
1
∑
n
lo
g
10
f
(
k
)
=
1.
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