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Austrian MO National Competition
1990 Federal Competition For Advanced Students, P2
2
inequality with integers
inequality with integers
Source: Austria 1990
July 10, 2009
inequalities
inequalities unsolved
algebra
Problem Statement
Show that for all integers
n
≥
2
n \ge 2
n
≥
2
,
2
3
4...
n
n
4
3
<
2
\sqrt { 2\sqrt[3]{3 \sqrt[4]{4...\sqrt[n]{n}}}}<2
2
3
3
4
4...
n
n
<
2
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