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4
classic telescopic, f(x)=4^x/(4^x+2) - 1985 Greece MO X p4
classic telescopic, f(x)=4^x/(4^x+2) - 1985 Greece MO X p4
Source:
September 8, 2024
algebra
Sum
Problem Statement
Consider function
f
:
R
→
R
f:\mathbb{R}\to \mathbb{R}
f
:
R
→
R
with
f
(
x
)
=
4
x
4
x
+
2
,
f(x)=\frac{4^x}{4^x+2},
f
(
x
)
=
4
x
+
2
4
x
,
for any
x
∈
R
x\in \mathbb{R}
x
∈
R
a) Prove that
f
(
x
)
+
f
(
1
−
x
)
=
1
,
f(x)+f(1-x)=1,
f
(
x
)
+
f
(
1
−
x
)
=
1
,
b) Claculate the sum
f
(
1
1986
)
+
f
(
2
1986
)
+
⋯
f
(
1986
1986
)
.
f\left(\frac{1}{1986} \right)+f\left(\frac{2}{1986} \right)+\cdots f\left(\frac{1986}{1986} \right).
f
(
1986
1
)
+
f
(
1986
2
)
+
⋯
f
(
1986
1986
)
.
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