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Chile National Olympiad
2024 Chile National Olympiad.
1
Antoher funcion.....
Antoher funcion.....
Source:
October 23, 2024
Chile
algebra
Funcion
function
Problem Statement
Let
f
(
x
)
=
10
0
x
10
0
x
+
10
f(x) = \frac{100^x}{100^x + 10}
f
(
x
)
=
10
0
x
+
10
10
0
x
. Determine the value of:
f
(
1
2024
)
−
f
(
2
2024
)
+
f
(
3
2024
)
−
f
(
4
2024
)
+
…
−
f
(
2022
2024
)
+
f
(
2023
2024
)
f\left( \frac{1}{2024} \right) - f\left( \frac{2}{2024} \right) + f\left( \frac{3}{2024} \right) - f\left( \frac{4}{2024} \right) + \ldots - f\left( \frac{2022}{2024} \right) + f\left( \frac{2023}{2024} \right)
f
(
2024
1
)
−
f
(
2024
2
)
+
f
(
2024
3
)
−
f
(
2024
4
)
+
…
−
f
(
2024
2022
)
+
f
(
2024
2023
)
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