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National High School Mathematics League
1986 National High School Mathematics League
9
Function Calculation
Function Calculation
Source: 1986 National High School Mathematics League, Exam One, Problem 9
February 24, 2020
function
Problem Statement
f
(
x
)
=
4
x
4
x
+
2
f(x)=\frac{4^x}{4^x+2}
f
(
x
)
=
4
x
+
2
4
x
, then
f
(
1
1001
)
+
f
(
2
1001
)
+
⋯
+
f
(
1000
1001
)
=
f(\frac{1}{1001})+f(\frac{2}{1001})+\cdots+f(\frac{1000}{1001})=
f
(
1001
1
)
+
f
(
1001
2
)
+
⋯
+
f
(
1001
1000
)
=
________.
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