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International Contests
Austrian-Polish
1991 Austrian-Polish Competition
7
7
Part of
1991 Austrian-Polish Competition
Problems
(1)
max of f (x) = \frac{x + x^2 +...+ x^{2n-1}}{(1 + x^n)^2}
Source: Austrian Polish 1991 APMC
5/1/2020
For a given positive integer
n
n
n
determine the maximum value of the function
f
(
x
)
=
x
+
x
2
+
.
.
.
+
x
2
n
−
1
(
1
+
x
n
)
2
f (x) = \frac{x + x^2 +...+ x^{2n-1}}{(1 + x^n)^2}
f
(
x
)
=
(
1
+
x
n
)
2
x
+
x
2
+
...
+
x
2
n
−
1
over all
x
≥
0
x \ge 0
x
≥
0
and find all positive
x
x
x
for which the maximum is attained.
function
max
algebra