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1987 Tournament Of Towns
(147) 4
TOT 147 1987 Spring Main S4 \sqrt{2\sqrt{2}{\sqrt{3}\sqrt{4 ...}}} <3
TOT 147 1987 Spring Main S4 \sqrt{2\sqrt{2}{\sqrt{3}\sqrt{4 ...}}} <3
Source:
April 17, 2020
inequalities
radical
algebra
Problem Statement
For any natural
n
n
n
prove the inequality
2
2
3
4...
n
−
1
n
<
3
\sqrt{2\sqrt{2}{\sqrt{3}\sqrt{4 ...\sqrt{n-1\sqrt{n}}}}} <3
2
2
3
4...
n
−
1
n
<
3
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