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National and Regional Contests
Bangladesh Contests
Bangladesh Mathematical Olympiad
2019 Bangladesh Mathematical Olympiad
4
4
Part of
2019 Bangladesh Mathematical Olympiad
Problems
(1)
BdMO National Higher Secondary 2019/4
Source: BdMO National Higher Secondary 2019/4
3/4/2019
A
A
A
is a positive real number.
n
n
n
is positive integer number.Find the set of possible values of the infinite sum
x
0
n
+
x
1
n
+
x
2
n
+
.
.
.
x_0^n+x_1^n+x_2^n+...
x
0
n
+
x
1
n
+
x
2
n
+
...
where
x
0
,
x
1
,
x
2
.
.
.
x_0,x_1,x_2...
x
0
,
x
1
,
x
2
...
are all positive real numbers so that the infinite series
x
0
+
x
1
+
x
2
+
.
.
.
x_0+x_1+x_2+...
x
0
+
x
1
+
x
2
+
...
has sum
A
A
A
.
algebra
inequalities