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National and Regional Contests
Vietnam Contests
Vietnam National Olympiad
1976 Vietnam National Olympiad
6
6
Part of
1976 Vietnam National Olympiad
Problems
(1)
Σ1/x_i^n from i=1 to i=k \ge k^{n+1} when Σx_i=1
Source: Vietnamese MO (VMO) 1976 P6
8/20/2018
Show that
1
x
1
n
+
1
x
2
n
+
.
.
.
+
1
x
k
n
≥
k
n
+
1
\frac{1}{x_1^n} + \frac{1}{x_2^n} +...+ \frac{1}{x_k^n} \ge k^{n+1}
x
1
n
1
+
x
2
n
1
+
...
+
x
k
n
1
≥
k
n
+
1
for positive real numbers
x
i
x_i
x
i
with sum
1
1
1
.
algebra
inequalities
Inequality