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Moscow Mathematical Olympiad
1953 Moscow Mathematical Olympiad
238
238
Part of
1953 Moscow Mathematical Olympiad
Problems
(1)
MMO 238 Moscow MO 1953 inequality with 2-\sqrt{2+\sqrt{2+...+\sqrt{2}}}
Source:
8/9/2019
Prove that if in the following fraction we have
n
n
n
radicals in the numerator and
n
−
1
n - 1
n
−
1
in the denominator, then
2
−
2
+
2
+
.
.
.
+
2
2
−
2
+
2
+
.
.
.
+
2
>
1
4
\frac{2-\sqrt{2+\sqrt{2+...+\sqrt{2}}}}{2-\sqrt{2+\sqrt{2+...+\sqrt{2}}}}>\frac14
2
−
2
+
2
+
...
+
2
2
−
2
+
2
+
...
+
2
>
4
1
inequalities
radical
nested radical
algebra